The bottlenose dolphin (Tursiops truncatus) was an aquatic mammal indigenous to Earth. It was a cetacean species.

When Spock tried to match the sound of the Whale Probe to the sound of an Earth animal using the phylum search mode from HMS Bounty's computer database, a bottlenose dolphin was one of the animals shown. (Star Trek IV: The Voyage Home)

Harry Bernard successfully carved a wooden statue of a bottlenose dolphin with a device that emitted a pink/orange beam while in the forced custody of the Aldean natives Accolan and Leda. (TNG: "When The Bough Breaks")

In 2365, a turbolift door close to a holodeck entrance was labeled Tursiops crew facility. (TNG: "We'll Always Have Paris"; [1])

The Star Trek: The Next Generation Technical Manual indicates that the dolphins were part of the Enterprise-D's complement, serving as navigational specialists. This would indicate that they were, in fact, a sentient species. They likely operated out of Cetacean Ops. Enterprise