Is anybody familiar with American/New York laws pertaining to rape/sexual assault, specifically to hospital protocol and whether/when police would get involved?

I'm trying to figure out if the hospital protocol changes for rape victims who come in on their own to report a rape and/or to get a forensic exam done, versus someone who's brought in via ambulance and who has been severely injured and is possibly unconscious. Would they collect partial evidence before surgery? Or would they still wait until the victim was conscious to gain written consent?

I'm also wondering if police would be called by the hospital if the victim was disabled (spoiler: it's Matt). I've tried to find literature on this, but mandated reporting mostly alludes to abuse of minors, the elderly, and people with cognitive or mobility disabilities, so I don't know if the hospital would go over Matt's head like that and contact police without his consent.

Also, does the American/New York State legal system differentiate between sexual assault and aggravated sexual assault (i.e, committing a sexual assault that wounds, maims, disfigures or endangers the life of the victim)?