tubman,
Whether or not a Model A either produced or sold new after December, 1931 was titled as a '31 or of the year in which it was sold would depend on the jurisdiction where it was titled. Today and for a long time, at least in the U.S., it is illegal to sell a vehicle as something more current than its actual model year, but there are examples out there that demonstrate that that may not have always been the case. In part it would depend on the honesty of the selling dealer as demonstrated by the paperwork that they provided to the buyer from which the title was obtained. Also, there were at least two major car market states (Illinois and New York) at that time that did not issue titles, only registrations which could add to the confusion.
Years ago, A good friend of mine encountered a great example of a dealer fudging model years to avoid a loss on an unsold prior model year vehicle. He saw a used 1954 Corvette for sale in the local paper and was interested in buying it and knew enough about the minor differences between the '53s and '54s to know that it was in fact a '53 sold new and titled as a '54. He bought the car and wisely wanted to have it re-titled as a '53. He started with the original selling dealer who was no help, likely because he did not want his malfeasance exposed. My friend turned to his state's title office headquarters and found little interest in righting this wrong even though the car's VIN was clearly within the range of published '53 Corvette VINs available from GM. He then appealed to GM directly and they proved helpful giving him all that he needed to convince his state's title people that the car was indeed a '53 and a new title was issued accordingly. I'm basically ignorant of stovebolts by choice, but not so much so that I was ignorant of the difference in worth between a '53 and '54 Corvette, even thirty years ago. (I recall that the original selling dealer ended up in a lot of hot water with both GM and the state title people.)
And then there are all those period examples of where model years spilled over into the following calendar years (1932 Fords were still being produced at one U.S. assembly plant in January, 1933 and abroad as late as 1936, for example).
In other words, I doubt if there is an all-encompassing answer to your question.
