Would your search- and browser history put you in trouble?

I saw a TV show some days ago about a murder case and the probable killer that was on the streets still despite a truck load of circumstantial evidence.
Amongst that evidence were data from his cellphone and his PC, like browser- and search history.
My question: If one of your neighbors went missing and the police, for whatever reason, came to your door to investigate you, would you be worried whether your search- and browser history and -behavior would get you into trouble (for example you searched for Duct tape and bin bags)?
But you didn’t have anything to do with the going missing of that neighbor.