Well, here's the thing... when it comes to the legal side of it, sex crimes are already under-investigated. In fact, that they are often not taken as seriously as they should be often just adds to the trauma of the incident. So any physical assault is going to be far more realistic if you want an in-depth investigation and a frustrating lack of evidence.
Furthermore, there is a very real phenomena that some people who are sexually assaulted feel incredible shame and embarrassment. This is extremely common with abused men, so much so that they will not only just avoid reporting it, but do anything they can to avoid anyone finding out about it.
If you want to make your story feel more authentic, make the abuse some type of physical assault that would logically warrant a full investigation. This satisfies your desire to get the police involved. Also include a sexual assault, but make that more personal. Maybe she even recorded it and taunted him with it. Now this gives your male character a very strong motivation to find her before the police -- he's ashamed of whatever sexual thing was done to him and needs to find her FIRST.
EDIT: I should clarify that the above actually solves the problem in your initial question. It doesn't matter whether or not the woman drugs him. She just needs to gain control of him somehow and then commit the assault. Maybe she gets him drunk then ties him up. Or coerces him at gunpoint. It can be whatever.
Furthermore, you can then also get your male character to do some of the work for you: Maybe he's so ashamed of whatever was done to him sexually that even HE tries to hide the evidence of it - he doesn't cover up the physical assault, but he tries to do everything he can to avoid the investigation steering toward something sexual.
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