There are no restrictions as to which District you can fly in. If it is an AMA sanctioned event, any AMA member can fly in the contest if they have an airplane that meets the requirements for that class.
'Districts' as far as pattern contests are concerned are usually referred to as the NSRCA (National Society of Radio Controlled Aerobatics) district where the contest is located. That may or may not be the same as the AMA district for that site. The NSRCA is the SIG (Special Interest Group) recognized by the AMA as the guiding organization for US Pattern.
Regardless, you are most welcome to fly at any AMA sanctioned pattern contest in any state whether you are a member of the NSRCA or not.
For information regarding the NSRCA, go to
www.nsrca.us
Woodie