Officers found two women and one man dead in an apartment. A man with gunshot wounds was taken to John Peter Smith Hospital in Fort Worth. He is expected to survive.
Richard said at least one witness identified the suspected shooter as the husband of one of the slain women. The couple was estranged.
Authorities went to the suspect's Arlington home and found him in the garage with what appeared to be self-inflicted cuts on his arms and neck.
He was taken to Medical Center of Arlington in critical condition.
Police, who declined to release any names, continue to investigate.