I would call the office asap because unless your dog has a microchip they will try to get your dog into a new home. Otherwise if he's neutered, has had his rabies shot and etc it could cost as low as 40 dollars plus 15 to insert a microchip if he doesn't have one already. Also, it's import to bring proof of ownership. They might challenge your attempt to reclaim if your dog doesn't have a microchip with the information to use as back up.
It will depend on how long he's been there, license status and whether he's neutered or not among other things. There are.many variables.
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