Boiling will change it a bit depending on how long you boil. It will let some gases escape and if boiled long enough so that a lot of water vapor is lost, the mineral content will be somewhat stronger. But to make a lot of difference will take lots of boiling. Look at the inside of an old tea kettle for an extreme example of what boiling leaves behind.
I guess my first question might be why you would boil tap water?
Part of the answer depends on what is in the tap water. City water with chlorine, or city water with chloramine, or neither?