This is US-specific, but anywhere in the US will do--I just need a general idea. Most of what I found was on missing children or missing mental patients.
I have an adult (19) who goes missing. She leaves her dorm room between 8:00 pm (when her roommate leaves for coffee) and 9:10 (when her roommate returns). The roommate assumes she's gone to the dining hall or out with friends, but it strikes her as strange that the usually antisocial girl doesn't come home all night, and by the time she gets home from classes at 1:00 the next afternoon she's worried. She consults the RA, who calls the girl's mother to see if she came home the night before or otherwise notified her parents where she went. Of course, she didn't, so panicked mother then calls the hospitals and eventually the police.
In my home city it's 24 hours before a missing persons report can be filed, and I think I've heard similar things about other US cities. As I said, I found a lot of information about missing children and mental patients, but this girl was 19 and believed to be of sound mind. There was no evidence of foul play, but she did not take things with her that indicated she intended to be gone for an extended period of time. Leaving for more than an hour without some kind of indication where she's going is EXTREMELY uncharacteristic for the girl in question, but I imagine that would be more significant to the roommate and mother than to police (Just the facts, and all that).
How might police respond when she's reported missing? Would it not be taken as seriously as an "emergency" missing persons report? Would someone come out in person to ask questions, or would the mother/roommate just fill out the proper forms? How long before a serious search was undertaken? I read on a UK site that bank account activity was one of the first things to be checked; what are some other things that would be looked at?