There are very few absolute rules in employment law. The right recommendation in one circumstance might be wrong in another. In case of doubt, the best step is to contact an attorney who practices employment law.
Of particular concern in this economy is preserving the right to collect
unemployment benefits. The two primary grounds for denial of benefits are voluntary resignation and misconduct connected with work (burden of proof on employer). If you are considering resignation and anticipate needing unemployment benefits, it is important to be able to establish that your resignation was not genuinely voluntary which can be difficult to prove or to reach an agreement with your employer that it will not contest your application for benefits. The employer's agreement not to object does not mean you will receive benefits, but makes it far more likely.
The following are intended as guideline:

1. Review your company policies.
Although New Hampshire law does not require employers to maintain policies, most companies, particularly mid-size and large companies, do so. Often they are available to employees on the Web. Unfortunately, under New Hampshire law these policies are not binding on the employer if the company has a disclaimer - - which most do - - stating that the policies are not binding. Nevertheless, the policy handbook provides guidance particularly in regard to the procedures for filing complaints.
2. Review your personnel file.
New Hampshire law guarantees you the right both during and after your employment, to review and receive a copy of your personnel file, and to have placed in your file your rebuttal to any negative documentation. This law is administered by the New Hampshire Department of Labor which broadly defines what should be contained in a personnel file.
3. Maintain notes.
It can be helpful to keep notes of issues occurring at work when those issues happen so you will not have to rely entirely on your memory should you later bring a legal claim.
However, it is important to understand that if you do bring a lawsuit, the employer may be entitled to a copy of these notes unless you were requested to keep them by your lawyer in which case it can be argued that they are attorney/client privileged information. In my experience, there have been as many cases in which notes later proved harmful to the employee in litigation, as cases in which they were helpful.
4. Filing an internal complaint.
Most employers have policies in terms of how and to whom a complaint should be filed with particular reference to sexual harassment. If you file a complaint, it is important to file it in writing or electronically, and maintain a copy should there later be an issue over the existence, subject matter or date of your complaint. The risk in filing a complaint is the potential for retaliation. If the complaint is about a violation of law such as sexual harassment or conduct in violation of public policy such as health and safety violations, then you are legally protected against retaliation if you can prove a connection between the retaliatory act and the complaint. On the other hand, if you make a complaint about an issue that does not raise legal issues, such as a personality dispute with a coemployee, the complaint is not legally protected, and accordingly, you may be subject to retaliation without legal protection. Whether filing a complaint is prudent depends upon the weighing of many factors including your own priorities. If you do not file a complaint and decide to raise the issue later, an employer may argue either that the problem did not exist or that it was denied an earlier opportunity to rectify it.
5. Consulting Administrative Agencies.
There are a number of federal and state agencies which may provide advice regarding your legal rights including the following:

FEDERAL AGENCIES
• Department of Labor (617) 788-2800
Wage and hour, pension and other issues.
• Equal Employment Opportunity Commission
Federal discrimination law. (617) 565-3200
• OSHA (617) 565-9860
Issues of workplace safety.
• NLRB (617) 565-6700
Collective bargaining, union organizing and collective activity.

STATE AGENCIES
• Department of Labor (603) 271-3176
Wage and hour, overtime, worker's compensation, and other issues.
• New Hampshire Commission for Human Rights (603) 271-2767
Issues of discrimination
• Department of Employment Security (603) 224-3311 or 1-800-852-3400 - unemployment benefits

6. Participating in investigations.
You may be called upon to answer questions as part of an investigation into concems raised by you, other employees or by the employer. Your participation in these investigations is legally protected against retaliation at least to the extent that the investigation relates to an issue that is protected by law or public policy. In general, the employer has the right to require you to answer questions relative to your employment, so refusal to participate in an investigation, whether it targets you or another employee,
can be grounds for termination. However, there is a law that limits polygraph exams. If you are asked to undergo one, you should consider consulting with an attorney. With the possible exception of situations when you are represented by a union, you do not have a right to bring a witness to your interview although it may be a good tactic to make that request.
7. Seeking other employment.
There is no legal prohibition against seeking other work provided that you do not disclose confidential information regarding your own employment. If you are dissatisfied with your current employment, looking for another job even while you are still employed, may be the best strategy. However, if your employer finds out, it could terminate you for job hunting, and unless you had a contract you would probably not have legal recourse.
It is not a good idea to use your work-issued computer, smartphone, etc. in your job search. If you signed a covenant not to take other employment in the same industry, you should consider seeking legal advice on the validity of the covenant.
8. Providing medical records.
If you are requesting medical leave or accommodation, the employer has the right to ask you for medical documentation. Many medical offices prefer not to provide specific medical information in order to protect your privacy. But the lack of specificity can be harmful if you later make a legal claim based on your medical condition. Particularly if you are pregnant and have an absence related to your pregnancy, you should let your employer know it is pregnancy related because the law provides additional protection for such absences.

1. Use a tape recorder in the workplace.
New Hampshire has a strict wiretap law which makes it a violation of criminal law as well as a civil offense to tape another without that person's permission including taping in the workplace. You could ask an employer to permit you to tape record a meeting, but it is unlikely that it will agree, and it is not legally required to consent. Generally, even the most damaging tape recordings are more of a detriment if a law suit is filed than a benefit.
2. Taking a copy of employer records.
Except for personnel records directly relating to your employment, all other records, whether in paper or electronic form, are considered the exclusive property of the employer. Although it may be tempting to make a copy of incriminating records or transfer them to your personnel computer, that action could itself be considered a sufficient infraction to justify your termination, and could nullify an otherwise valid case.
If you file a legal claim, you should be able to secure a copy of those records during the course of litigation. Although there is no guarantee that the employer will not destroy those records, that is difficult to do and could be very damaging to the employer's legal position.
3. Use of your employer issued computer, smartphone. etc.
Many employees use their work issued devices for personal purposes, and believe that personal communication will remain private. However, under the law, the employer ispermitted to have a policy where it can monitor and review all communication on work issued devices even when that communication occurs outside of the office and is unrelated to work. It is more prudent not to communicate about personal and particularly legal issues on company owned devices.
4. Discussions with co-employees about complaints in the workplace. In theory, your discussions with other employees about issues in the workplace may be legally protected as collective activity under the National Labor Relations Act or as protected activity under a particular law which you are claiming was violated. However, as a practical matter, if you file a claim against your employer, other employees who still work there could be under substantial pressure to testify against you. There is a significant risk that any co-employees with whom you discussed your legal concerns either misinterpret those conversations or distort them to your detriment during your employment or in a subsequent legal proceeding.
5. Use of social media outside the workplace.
Most people assume that their communication on their own computers and other devices outside the workplace cannot be used against them in their employment. However, at least for most employees at will (without contracts), the employer does not need a good reason to terminate an employee and may be inclined to do so if it receives information that the employee is being critical of it on Facebook or other media sites, or makes admissions of personal misconduct, etc. Although the National Labor Relations Board takes the position that criticism of an employer on Facebook or other media can be protected concerted activity, it is risky to rely on this legal protection.
6. Resignation.
Whether you resign is a personal decision that goes well beyond legal considerations. However, if you are considering resigning because of potential legal issues in the workplace, it is important to consult with an attorney prior to resigning, since your resignation could have a substantial effect on your potential legal claim. It could also undercut your attorney's ability to negotiate on your behalf. Additionally, a resignation, when genuinely voluntary, would likely disqualify you from unemployment benefits.