Are there Constitutional limits to police investigations other?

[Kermit the Rock]

than Search, Seizure, and Interrogation. Can police spend as much time investigating a person on suspision that a crime, with no actual evidence of any crime, as long as he doesn't exceed those three areas of protection.

Seems like an Officer could do a lot of investigating without having to involve the person at all-facebook, websites, NCIC, court databases, property records.