Normally you should specify the folder containing the database as |DataDirectory| in the connection string, e.g. "Data Source=|DataDirectory|\MyDatabase.mdb" and that will resolve to the correct location at run time. While debugging it will resolve to the same folder as the EXE was run from.
Once released, it depends how you deployed your as to what path |DataDirectory| resolves to. If you just copied the EXE then it's the same as when debugging. If you used ClickOnce then ClickOnce will manage that and you don't have to worry.