You do not state how old the car is, I am assuming it is less than 10 years old. In this case, most of the cars have their own internal communications system, which in this case monitors several inputs to determine if the car is being stolen. So IMHO, I am guessing that one of these inputs (door ajar, key in the ignition, hood ajar, vibration, tilt, etc sensor) is defective, causing the computer to say Hey I am being stolen.
I had a Chrysler Sebring convertible that did something very similar. Initially the dealer quoted repairs and replacements that would have totaled over $1200, not including the towing!! After some additional discussion the dealer told me to try disconnecting the battery FOR OVER 1/2 HOUR, to completely clear all codes, etc. This actually worked, unfortunately, whatever was causing the problem, continued, and I had to do this 2-3 more times until I sold the car. I did mention to the buyer this quirk.
Hope this helps.
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Pennsylvania, for 60+ years, most recently, Allentown, now TV. 
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