Don't make the mistake of assuming that your obligation to investigate a harassment complaint ends when the victimized employee quits.
Reason: The U.S. Supreme Court just ruled that employees who suffer a "constructive discharge", meaning they felt forced to quit because of intolerable working conditions, have the same rights to sue for harassment as employees who are fired. (Still, the ruling is a mixed bag because, as you'll see, it does provide a way for businesses to defend themselves.)
The Supreme Court ruled a few years ago that if one of your supervisors does the harassing, your organization can be liable if the harassed worker suffers an "adverse employment action," such as firing, pay cut or demotion. This new ruling effectively adds constructive discharge to the list of adverse actions that can spark liability.
As a result, if employees quit and say it's because of harassment, you should immediately launch an investigation. Document your probe, discipline the harasser (if appropriate) and notify the ex-employee of the investigation's results. If you find the employee's harassment complaint is legitimate, extend an offer to return to work, along with an assurance that you intend to provide a workplace free of harassment.
Recent case: Police dispatcher Nancy Drew Suders resigned, saying that she felt forced to quit because of daily sexual harassment from male supervisors. She said supervisors discussed sex and made obscene gestures. She sued for sexual harassment, and this high court ruling allows her case to go to trial.
Can you defend yourself against such claims? Maybe. Your organization can defend itself by showing it had effective anti-harassment policies and procedures, and the employee didn't take advantage of the complaint process. But you won't be able to use this defense if the harassing supervisor engaged in an "official act" (such as demotion or pay cut) that contributed to the employee's resignation. In such cases, where a forced resignation is paired with an "official act," your organization is automatically liable, without any defense, as long as the case facts are proven. (Pennsylvania State Police v. Suders, No. 03-95)