Your next question might be:
Q. Do I have to pay state income tax to that other state, for the week I worked there?
A. Yes, but "nobody" does. See http://money.cnn.com/2013/06/28/pf/taxes/business-traveler-tax-threat/ If you live in a state without an income tax (e.g. FL or TX), it’s more likely you should file in the work states. You can't use the "it all comes out even" rationale for not filing.
