Police have released a 23-year-old woman on bail after she was questioned on suspicion of wounding.
Officers found her with stab injuries to her arm, after they were called to Upper Seymour Street, Barkerend, on Sunday, after a car was reported as stolen.
A 29-year-old man attended Bradford Royal Infirmary with stab wounds. He was detained overnight for treatment.
Inquiries are ongoing to locate the car, a black Audi A3, FW12 0OX. Anyone with information should call Bradford CID via 101.