However, should you be able to access these records it would clearly indicate whether or not a permit was ever pulled for the room in question. If there is no signs of a permit but one is required to legitimize the addition for the square footage of the appraisal you should see it the current owner would be willing to do that. It would be in both of your best interest to do so.
He would gain from added square footage which would add to the value of the appraisal and you would gain likewise albeit the current owner would then be able to add value to the sales price. Now if the home is an REO or a short sale all bets are off as it would not be very likely that the bank or the in arrears homeowner would be willing or motivated to put in any time, money or effort.
However, if you really like the home and you think you're getting a good deal then I certainly wouldn't let that stand in your way. I've seen a lot of real buying opportunities evaporate over some pretty petty issues. I've actually been down that road a few times myself. If this home gives you warm fuzzies I say pull the trigger.
Without going through all the hassle of going down to the city (the answers below seem to presume that you are i contract on this home. If you are not, don't go running to the city until you are.) Goto county records and see what that has to say. ON county records, the number of rooms, beds and baths should sync up with the home of interest. If it does not, you can then make an inquiry to the owner via agents.
Happy funding, Rudi