Luckily you seem to be in a specific, limited situation so you don't need to consider things such as non-human actors (Lassie, for example) or multiple producers (in reality, movies can have more than one producer).
Despite the limitations, I would allow a person to be both an Actor and a Producer (as, for example, DiCaprio is irl). Plus I would design to allow for other categories to be added later, such as Director or Guest Star. Therefore:
(1) rather than putting "EntityTypeId" (a rather awkward name too, btw) in the Persons table, I would have a separate table with MovieId, PersonId and EntityTypeId (yes, all three, see #2 below for why)
(2) meaning instead of a Movie_Actor table, say a Movie_Persons table, which includes the EntityTypeId. That is, for each movie, specify whether the person was an actor or producer (or perhaps both!) for that specific movie, rather than pretend a given person could only be one or the other for every movie.
sorry to bother you .I have one small question .I'm quite new to SQL and entity framework.I want to develop API's for only actors or only producers but we don't have any relation of person -> role