Dogs are allowed on patios that are not enclosed by law, however enclosed patios have enjoyed some laxity.
When we were in Silverlake we were THE dog friendliest place to go. We're still dog friendly and even have free doggie treats (and some free horsie treats from time to time) on the bar in the window, but we have far less space outside for our furry patrons.
On a related note - I had one health inspector tell me that therapy animals are always exempt. She went so far as to tell me that someone could even have a therapy rat and there was nothign the health dept could say about it. No one has ever gone that far, just so you know

We HAVE had some shoulder riding parakeets from time to time.
Deborah - The Back Door Bakery