Yes. There do not have to be witnesses to sue for sexual harassment.
However, before you sue for sexual harassment, you should first complain to your supervisor or to the appropriate person designated in the harassment policy in your workplace.
For example, say you have a boss who is harassing you in private. No one else knows about it. You go to his or her boss or to the appropriate HR person and complain. Once you report the harassment, the employer is required to do an investigation.
The employer would, of course, ask you, “Are there any witnesses?” to which you would reply, “no.” The employer would then interview the harasser; however, the harasser may very well deny that any harassment has occurred. The employer will then have to make a decision. Often the employer will hire an outside person, such as an independent investigator, to come in and take the investigation over.
Whoever is in charge of investigation makes the determination about whether or not the harassment charge has been substantiated. If there are no other witnesses, it’s possible that your employer or the investigator could decide they could not substantiate your charges because you said one thing, your boss said another thing, and they couldn’t really decide who to believe or there wasn’t enough evidence to substantiate your claim.
This does not mean you don’t have a legal claim; however, in any court situation you must have enough evidence to prove the case to the jury. If you don’t have any witnesses, you’d have to have a very convincing story or some other evidence to substantiate your claim and to make it clear the harassment happened.