Does anyone know the answer?

I remember seeing people walking dogs on the beach last time I was there....didn't see many and can't tell you if they are "officially" allowed.

Pet parks and pet approved beaches:

Sarasota is a very friendly pet area, although there are no dogs allowed on Siesta Key Beach, there are several parks and beaches dogs are allowed on;

Parks/Beaches which allow pets. (Animals must be on leashes):

Bird Key Park on the John Ringling Causeway. (Beach front)
Ken Thompson Park - 1700 Ken Thompson Parkway. On City Island, by Mote Marine Lab. (Beach front)
Bay Front Park. U.S. 41 and Ringling. Next to Marina Jack Restaurant. (Some water)
Gillespie Park. 710 N. Osprey Avenue. Downtown at Gillespie and N. Osprey.
Arlington Park. 2650 Waldemere Street. Near Tamiami Trail.

GoTravel, You seem to know a lot about Siesta Key. Thanks for the info. Do you also know of any beachfront rentals on Siesta Key that take dogs? We desperately want a view of the Gulf. And of course we also desperately want to bring our pooch!

I checked my "Dog Lover's Companion to Florida" and it lists four places on Siesta Key that allow dogs: Heron Lagoon Club, Surfrider Beach Apartments, Tropical Breeze Inn, and Turtle Beach Resort. (You can do a web search to get info on these.) It also says that on the south end of Siesta Key, Turtle Beach doesn't officially allow dogs but dogs are "very much tolerated."

You can probably also check some of the pet friendly lodging websites.