A man who allegedly tried to drown a police dog in a creek as it pursued him in Melbourne's north on Wednesday night has been arrested after seeking treatment for serious dog bites.

Police said they pursued a white sedan early on Thursday morning and arrested a man and a woman in Reservoir after a tyre on the car blew out.

A second man fled into the nearby Darebin Creek and four-year-old German shepherd, Indy, chased after him.

Police said a 19-year-old Broadford man hit Indy on the head and then attempted to drown the dog, but was bitten.

A police officer pulled Indy from the water but the man escaped.

The man was arrested later in the morning when he sought treatment for severe dog bites at hospital. He remains in police custody.

Police charged a 20-year-old Pascoe Vale woman with conduct endangering life, handling stolen goods and traffic matters.

A 29-year-old Mill Park man was released pending further inquiries.

Indy was checked by handlers and is now back on duty.