You may not hold a Canadian and American license simultaneously.
Noy quite trure. You may not hold 2 state or 2 provincial Dls, but unless the particualar state has an agreement with province to capture DL, you can keep it after getting state DL.
But, regardless, as MC sez, you need a DL where you live, and unless you are a student, most states consider a person living and working in a state as requiring DL from that state.