Thelma Todd's autograph is not particularly rare compared to that of some other stars of that era. She would sign things for fans. The only thing that would tend to make her autograph difficult to find would be it's age.
An early photograph supplied by the studio with a printed autograph.
This was probably a black and white photo that was colored afterwards.
Thelma Todd frequently used one letter "T" for both her first and last names, as in this example.
And here we have a few photos with a short message along with the signature.
This photograph was autographed by not only Zasu Pitts and Thelma Todd, but the photographer ( Stax ) as well.
A couple of notes from Thelma Todd that turned up on ebay.
Thelma Todd's autograph was reproduced in SCREEN ODDITIES, as were the autographs of many other stars of the day.