The logbook states a 1000kg tow rating if it comes with a factory fitted towbar. If this isn’t specced, the tow rating is 0kg, which means one can’t be retrofitted. The suggestion I’ve read is if the towbar isn’t specced, Tesla don’t bother fitting/welding on certain elements of the rear structure that are required to attach the towbar. In the case of the Y, the rear casting is one big piece, so is suitable to tow even with the standard part.I thought the model Y was always a retrofit at the SC unlike the model 3 (maybe because some of the receiving hardware has always been present from factory) hence the rating will be present in the logbook. Maybe owners with Model 3's (with factory fitted towbar) could chime in and say what is stated on their logbook.
Edit: I know a towbar can physically be retrofitted to the M3, however this isn’t suitable for towing and can only be used for bike carriers.