Can the police go after me just for searching people's names on Facebook?

[Samuel]

If they can prove you did it (which requires seizing your computer), they can't charge you with a crime on that basis; however, they can put it in their list of supporting facts for charging you with a crime RELATED to that conduct.

For example: if they obtained a warrant to seize and search your computer and discovered you stalked a girl on FB by the name of Shirley Temple several times a day for the past 6 months, they could use it in a case against you for the rape of Shirley Temple, which occurred two weeks before.