What constitutes illegal harassment?

Unfortunately yes, it is almost certainly. There is no law saying that supervisors have to treat their staff fairly, kindly, with respect, etc. They can be as nasty and suspicious as they like.

If there is an internal company policy against this sort of harassment or behavior, the supervisor may be in violation; or even if there's not some policy, if you think her bosses would disapprove, you could bring it to their attention anyway (though note: going over a supervisor's head could itself cause you trouble--some companies do not support that).

If you feel you are being harassed because of a protected category, such as your race, sex, religion, age over 40, or a disability, then you may have a workplace discrmination claim.