Though the actual risk is not great, people connected with an investigation should remember they could be sued, personally, if they go too far and end up interfering with someone else's rights. For example, if you restrain an employee from leaving the room or the employer's premises until he or she answers your questions, you could be sued for false imprisonment. Similarly, libel is possible if you distribute materials falsely accusing someone of a crime. Other torts are possible, as well. You should consider consulting with legal counsel when in doubt.
A sense of "fair play" is crucial. Private employers are often not subject to all of the "due process" restrictions imposed by the Constitution on public law enforcement officials, or public employers but you still can't take the law into your own hands. For example, you cannot restrain an employee who wants to leave; and you may not be allowed to coerce an employee into doing anything he or she doesn't want to do.
The question is ambiguous -- Ruth has answered some potential liability exposures that arise due to the manner in which the investigation is conducted. Also keep in mind that it matters if you are a public or private employer and if there is a CBA in effect or not. I can't think of anything immediately, but I suspect that there's a government contractor angle to this, too.
The other side of the coin is potential exposure stemming from the cause of investigation. For example, if there is an external investigation (whether internally or externally motivated), and they uncover, for example, that a person in power knowingly allowed sexual harassment to go on, that person has a personal liability exposure. There can be criminal penalties for payroll professionals who, for instance, knowingly short change the IRS, even if they do so under direct, written order of the CFO.
Your friends include liability insurance (many employment related risks are not covered), employment practices liability insurance (EPLI: covers the Company), and directors and officers liability insurance, if you have an officer title or are on the board of directors (D&O: covers the people). Of course, they may not cover willfull violations and, if they do, they will likely drop you from coverage after they pay off.
Can you elaborate about whether the investigation is being conducted internally or externally, if it was motivated by internal or external forces, and anything about what is being investigated?
Also in certain benefit plans (those covered by ERISA), depending on the circumstances, you could also possibly be considered a fiduciary. I am one on our 401k plan. However, your employer should be providing coverage like TXHRGuy stated to cover you in those situations.
http://www.milliman.com/expertise/employee-benefits/publications/wp/PDFs/i-think-im-fiduciary-WP02-01-08.pdf states very specifically that personal liability arises when there has been a fiduciary breach in a 401k plan
Honestly, I would sit down with an employment lawyer and an insurance agent to discuss the liabilities of the HR positions and make sure that you are covered because there are too many to rely on a forum to think of them all.
And not just for HR, but for supervisors. There is a lot of liability to spread around at a business.
Your company may want to look into Directors & Officers coverage, Employment Practices coverage, and Fiduciary coverage.
A few things you could easily be named as a defendent in are sexual harassment, FLSA, ERISA, FMLA, etc. etc. etc.