Austin,
The FFL you buy it from has to put down what it is sold as. Either it is a pistol frame or a rifle frame. They might sell you just a frame but it is designated as either a pistol or rifle.
They used to do that but currently if it comes as a bare frame, they don't designate it as a rifle or a pistol; just as a frame.
In addition, in those cases where the FFL holder has in the past designated a frame as a pistol frame, I believe that would be adequate for States that required handgun registration but I doubt it would change the fact, as far as the BATFE is concerned, that the frame was sold elsewhere originally as a rifle frame.
Also, I don't think T/C has "P" in the serial number of pistol frames. There is an "S" for stainless frames and "C" for camo frames. Who knows what blue frames have since I've never owned one. You can, however, call T/C, give them the serial number and they'll tell you in what configuration the frame was originally in when sold.