The lawsuit, filed Thursday, cites concerns at the Clinton-Peabody Housing Complex. It also names the company that manages the complex, McCormack Baron Management.
The lawsuit alleges that the problems have long been evident but have not been resolved.
Hawley, a Republican, is running for U.S. Senate against incumbent Democrat Claire McCaskill, who also has pushed for improvements at Clinton-Peabody. She toured the complex in April, when residents told her about problems, including severe mice infestations, that they said were addressed only after protests and media coverage.