Something to keep in mind is that your character is a main character in the story being told. Just another cop would stay at the office. The cop who is worthy of story is going to go where the adventure takes him. Your job as a PC is to come up with an in character reason for your cop to go along with the adventure.
(This is of course an oversimplification based on the games I've participated in. There are definitely games where what I suggest would not be the case. I suspect my experience is similar to the average gaming experience, but have no way to back this up. Part of being an experienced roleplayer is figuring out what kind of table you're playing at.)