|Chrysler Avanti 1963-1964|
If the film debuted in 1963, then it is probably in the public domain. If its debut was 1964, the film is very likely still under copyright. The reason: works first published before 1964 had to be renewed otherwise they became public domain. Only 15% of works were renewed so the odds that a B-picture from fifty years earlier was renewed is slim. However, works debuting in 1964 (and through 1977) did not have to be renewed and are protected for 95 years from publication date. (In the case of a 1964 film, that would be until 2059.)
What do you do? Under copyright law, the copyright registration for the film creates a presumption of ownership and you have the burden of rebutting that presumption. You will need evidence. An IMDB listing is helpful but not determinative. You would be better served with newspaper or trade advertisements or reviews. Also helpful would be the date of the copyright notice on the film or posters, as well as research performed by sites like Horrortheque. Finally, you should have a Copyright Office search performed to see if the film was renewed (only renewals for books are available online). All of this evidence gathering may put you off the project but it will all be necessary if the current copyright claimant comes after you and you need to defend your position.