You really would need to add many more facts. Documentary or not. Flattering light or not. Father alive or not.
The above is general legal and business analysis. It is not "legal advise" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
There are not enough facts in this question to properly answer your inquiry. In addition, use of likeness analysis is very fact specific. You should consult an attorney who is familiar with this area of law so that they can fully analyze your situation and advise you appropriately.
"Life story" rights can be tricky, especially if your father was famous and he had "publicity rights" that you inherited and control, if your state(or the state your father lived in) recognizes those kinds of rights, as CA and TN, to name two states, do.
Some state only recognize publicity rights in living people, in which case your permission would be irrelevant.
These publicity rights are balanced against the rights f the public to use historical facts and news for the public good, even if the uses are for profit. You haven't disclosed what kind of move this is, so that too, is a factor.
Since there aren't enough facts here to properly analyze the question, you'll need to sit down with your own lawyer and discuss the entire situation.
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There is not enough here to be able to respond. Please give more details so we may help.
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"More data please!" Likely yes as a practical matter and likely not as a legal matter. However, more facts are needed, such as:
1. How well known is your father?
2. Is your father alive?
3. Is your father running for political office? Is anyone in the movie running for office or holding office?
4. Is the movie a documentary, a commentary, an educational project, or some other special type?
5. Will the movie be for personal use or will it be sold?
So, best to see an entertainment or IP attorney so you can give "the rest of the story" and get the rest of the advice.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
The answer is that this depends on many facts and circumstances. New York recognizes a right of publicity but only for as long as an individual is alive----the right of publicity does not survive death in New York. In California, in contrast, the right of publicity survives death. In addition, the First Amendment allows persons to make biographical movies that tell stories about persons that may be interesting or newsworthy. There are thousands of biographical books and movies that are perfectly legal, and that are made without consent of the persons who are the subject of the book As long as the person who makes the film does not assert that the film is officially connected to, written by, or endorsed by the subjects of the film (in this case, your father), it is very unlikely that the film violates your parents' rights. Of course, the devil is in the details in a situation like this, and therefore, if you want to pursue this further, you need to retain IP counsel to advise you after reviewing all relevant facts and circumstances.