Hi again,
Dodge RAM 3spd auto transmissions (RWD) available for the 3.9L engine were:
3-Speed: A500 (42RH)
3-Speed: A727 (36RH), Sportsman Model
If you can't find your model code on the transmission casing, the vehicle build plate (in the engine bay) should have the factory drivetrain code stamped on it.
Failing this, Chrysler/Dodge should have your transmission details on their database.
If you end up replacing the entire transmission, you might as well upgrade to the improved 4-speed. Most Chrysler/Dodge RAM transmissions were a universal fit, but some had stronger internal components to withstand the higher torque of the larger capacity engines.
I've located a link which has more technical detail on the transmission:
http://www.scribd.com/doc/228727/Dodge-Trucks-TechTran-A500-42RH-A518-46RH-A618-47RH-Service-Manual
Cheers,
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