Perkins was bisexual. He was married to photographer Berry Berenson (1948-2001) from 1973 until his death from AIDS in Hollywood, Los Angeles, California in 1992. The couple had two sons, actor Oz (born 1974) and musician Elvis (born 1976). Berenson was killed in the September 11 terrorist attacks. She was aboard American Airlines Flight 11 when it was hijacked and crashed into the World Trade Center.