A few ways you may be able to find out.
1) Contact cadillac. I bet they have an archives & a historian that
could help. Probably can give you the dealer they sold it to & maybe
the first owner & build sheet.
2) contact the Calf DMV since it was sold there.
3) contact the DMV that the title was issued by & try to work back.
Start with Caddy. The states will charge you a title search fee !
Story.........
My late brother in law collected Hudson, Essex & Terraplane cars.
He bought an Essex ( I forgot the year ) to restore. He researched the car
& found that its was the same model / year & color as the car they sold or
gave to Amelia Earhart through the same dealer ! Never could prove it
beyond doubt. I may have ridden in her car......
BTW every state has its own rules for titles & registrations. Often
different names like in Ma its RMV ( registry of motor vehicles ) here
in N.H. its DPS ( department of public safety ).
73 Zeno
LFOD !