For the inside handle, check on the inside, where the handle would be against the door panel, there should be a small slot along side the shaft. With a small pic, you should be able to push back the spring plunger that locks onto the shaft, according to the "Fisher Body Service Manual", in front of me. The outside handle, has a machine screw straight into the end, of the inside end of the shaft. Sorry, I don't have a scanner, the pictures in the manual would be more helpful.
I'll see if I can scan some pages of these manuals, when I go back to work later this week, boy are they worth their weight in gold, when disassembling these old wood structured cars. I have a "Fisher Body Service Manual-1926 to 1931", "Fisher Body Service Man.-1932", "Master Parts Manual-1929 to 1931", Master Parts Price List-1932 w/ body wood diagrams, "Chevrolet Service Repair Manual,1929-1931"and owner's manuals for 1929 Chev car and 1934 Chev truck. If you need anything else feel free to ask.
I see the hole where the screw would have been, may just be galded together. That screw, as mentioned, does go in the back of the handle. Unscrew the latch from the door and see if that helps..
WOW, thanks for all of the replies, bitchin'! I have now removed all the handles and latches. All of the wood from the whole body and doors has been removed now also. I'm replacing all of the wood with steel. It's just nuts how these bodies were assembled. Lot's and lot's of work left...