If Stella and Lisa are Jeff's accomplices, then Det. Lt. Doyle is an obstacle, a skeptic who questions Jeff at every opportunity and tries to convince him that he hasn't seen what he's seeing. "I think you saw something that has a very simple explanation," he says, and he doesn't really give up that idea until the murderer is literally dangling Jeff out the window.
At least he seems competent enough: he and Jeff are good friends, and he's clearly a man of integrity, if not always of intelligence. He has a family at home, and he definitely wants to do the right thing. He just doesn't believe that Jeff has stumbled upon a murder, and while he answers a few questions and provides a few signposts, it's clear that he doesn't approve of Jeff's snooping ways. It's a waste of resources in his professional cop's mind, and he's not going to do that just to indulge an excitable friend.
Doyle's attitude comes from practical storytelling necessity. If Doyle believed Jeff, he'd assign some detectives to catch Thorwald, and then we'd have no movie. He keeps emphasizing to us that the police aren't getting involved in these little reindeer games, and if Jeff wants to solve the murder, he's going to have to do it himself.
But beneath that, Doyle has something subtler to say, something very near and dear to Hitchcock's heart: don't trust The Man. According to Hitch, his father brought him to the local police station as a boy and asked the cops to lock him up in jail as a punishment for something he did wrong. (Source) Whether that's true or not, Hitchcock definitely didn't like policemen, and his films sometimes show them in this negative light. (North by Northwest, for example, has the hero being unfairly pursued by the authorities for the whole film, while Psycho features a very scary cop following Janet Leigh for a while.)
At least Doyle comes through to wrap everything up at the end, the time-honored purpose of cops in movies like these. He's big enough to admit that he was wrong, preserving his friendship with Jeff and making sure Thorwald gets taken off to prison. Beyond that, he exists simply to challenge Jeff's assumptions and ensure that the mystery isn't solved too easily, making him a sympathetic pain in the butt but a pain in the butt nonetheless.