Newly released bodycam footage and transcripts show the man, Sean Bickings, 34, getting into Tempe Town Lake last month and warning police he was "going to drown".
But none of the officers on the scene intervened to save him, with one heard saying: "I'm not jumping in after you."
Mr Bickings soon slipped underwater and was later declared dead.
Describing him as "an unsheltered Tempe community member", city authorities called his death a "tragedy".
