Another FReeper made the suggestion of simply announcing that attendance is limited to residents of the district, and that people will be required to show drivers license with addresses in the district.
What some others holding events do:
Announce that the Town Hall is for those who live and vote in the congressional district.
Restrict attendance to ticket holders
Hand out free tickets in advance at the politician's local office or the office of the local republican club.
That gives the ticket administrators an opportunity to "Vet" those who ask for tickets.
Back when the democrats were holding Town Hall meetings to sell Obamacare they would open a side door or back door early to let the democrats in.
Then when the front doors were opened at the publicized start time most of the seats would already be filled with loyal democrats.
I know for a fact this happened locally because the local news ran interviews of people complaining about it.
Some aid they were among the first to be let in the front door only to find most of the seats already filled.
Others said that they were told no seats were available even though they got there early and were near the front of the line.