You don’t have to be a resident of a Congressional district to run, just a resident of the same state. However, it’s usually ill-advised not to live in it if you’re planning on running.
This just in:
CA CD-46: Irvine Councilwoman Lynn Schott (R) has quit open seat race; telling local blog she filed FEC papers but decided it was mistake.
With Schott out, there are currently NO GOP candidates in this race, including speculative, for Loretta Sanchez’s seat.