There is absolutely no requirement that a candidate for Congress live in his congressional district. Neither states or Congress have the authority to add additional qualifications to those specified in the Constitution (25 YO; US citizen for 7 years; and an inhabitant of the
state when they are elected; and the provisions of the 14th amendment dealing with former rebels).
It is sometimes a political issue. For example, in 2004, Martin Frost changed his residence so that he could run against Pete Sessions, but failed to update his residence for tax purposes (in Texas, there is a break on property taxes for an owner-occupied residence, as well as protection from debt collection).
Meanwhile the Frost campaign complained that Session had not lived in the district when he had been elected. Sessions had been elected in 1996 from District 5 that had included parts of North Dallas but then extended south towards Houston. The 2002 court-ordered redistricting had created a new District 32 in North Dallas including areas of Session's old district, and maintained other parts of District 5 as a continuing district. He lived outside the new district but ran for and was elected in the open seat. Meanwhile Jeb Hensarling was elected in the District 5.
In the 2003 legislative redistricting, District 32 was modified to include Session's residence.
