Here's an autographed photo of Carole Lombard now on sale at eBay. The signature appears genuine, and according to the seller, the image measures 5.5" x 7" -- a size more associated with pictures for autographs than for publicity stills sent out to newspapers or fan magazines.
There's no p1202 number to show it was part of Paramount's roster of Lombard poses. In fact, if you look at the lower right-hand corner, no name is seen printed, merely "...in Paramount Pictures" below where Carole would sign. So I'm guessing this was produced by the studio specifically for Lombard to send to fans. (Another hint: The "Cordially" begins to run out of ink near the end of the word, so I'm guessing Carole then found another fountain pen in which to sign her name.)
Note the date at the top -- May 22, 1935; according to the seller, that's the date the collector documented he received or obtained this. It would be consistent with times of similar poses Lombard shot for Paramount, such as p1202-864:
The seller also provides a certificate of authenticity:
As is the case for nearly every Carole autograph, the price is hefty...but at least this seller has a way to lighten the burden. You can get it straight up for $799.99, or for $134 monthly for six months (a difference of only $4.01). Interested? Then go to http://www.ebay.com/itm/Carole-Lombard-Sepia-Vintage-Matte-Finish-Signed-Photograph-/311335223087?pt=LH_DefaultDomain_0&hash=item487d067f2f