The Greek American activist was fatally beaten while trying to escape from a store in Athens in 2018.
Antonio Zephir says the neighbors have harassed him previously, and he is seeking a restraining order.
Martinez was shot at least five times; a man she believed was stealing from her is charged in her death.
The 18-year-old was robbed, had his penis partially severed, and was set on fire in Montego Bay, Jamaica, by three men.
She is at least the 40th trans, nonbinary, or gender-nonconforming person known to have died by violence in the U.S. this year.
Police say one student has been charged with the attack.
Authorities say there was a "good chance" the officer used her service weapon to shoot her ex-girlfriend and her ex-girlfriend's new partner.
