Extensive hail damage can cause your vehicle to be deemed a total loss and in that case then in most states the clean title would need to be turned in for a salvage or branded title. The same holds true for an accident with a deer. If the damage is substantial to the vehicle so that it is declared a total loss then the car would receive a salvaged or branded title in most states.
If your car is totaled out by either extensive hail damage or a run in with a deer the claim would be made through your Comprehensive coverage portion of your auto insurance policy. When your insurer pays out the Comprehensive claim on either a car totaled by hail damage or a deer then the car would usually be required to have on it a salvaged or branded title. If you choose to keep the car after the total loss (buy it back) then it may be required to have repairs made so that you can obtain a rebuilt title. In some states if the total loss is due to hail damage you may instead receive a hail damage title.
If the car is not totaled out but just sustains damages from hail or a deer and is repaired then the car should continue to carry a clean title. Your vehicle's history however may show the accident and repairs made depending upon the reporting system of your state. So while the car may have a clean title the accident with the deer or hail damage may show up on the vehicle's car history, such as the one someone can obtain from CarFax.
CarFax notes that their vehicle history can show accident or damage reported to them from various sources in reports they receive in from all states. It may include police-reported accidents, damage disclosures and collision repair facility reports though not all accidents or damage events are guaranteed to be found on the vehicle's history compiled from the information they receive in.
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