It is not harassment for a city/govt office to send you letters and notices about a potential violation, no matter how frequent. If the garage door was required to have a permit and did not, then you need to comply--it does not matter to them that you did not install it. You may have rights against the previous owner, but as between you and the city, it won't matter. If you feel strongly that you want to fight, enough to pay attorneys fees, then consult with a local attorney. Also, I'm not sure what you mean by "proof"--they usually have specifications in the codes stating what types of things a permit is needed for, if your garage door fits those parameters, then they're going to send out the notices. There's no "proof" really, unless they are to come to your door and measure the garage door--but I don't know how that helps you.
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I recently was involved in a county coding dispute. One of two things have happened. First, the county is wrong and no garage door was ever installed without the proper permit. You can make this point at a hearing they will set and they have to prove it was installed without a permit. You will be responsible for the costs and fees of this hearing should you lose. The second possibility is that the previous owner installed a garage door that was not coded properly. The liability for a code violation is on the present owner regardless of who actually initiated the violation. (for most counties) You will have to go to the county building department office and apply for the garage door permit. Once that is approved you will need to schedule the proper inspections. Inspections for a garage door may include electrical, structural and several others, but the building department will let you know. You then have to pay for and schedule the inspections. Once the inspections are completed you can apply for a certificate of occupancy. (if one is needed for a garage door, the county will tell you). As far as the letters, they are not harassment.
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