Okay, since your question is specifically about Harry Potter and the Chamber of Secrets the movie, I'm going to answer based only on the film and plot points from the film.
When Harry, Ron, and Hermione discover the first message written on the wall, when Filch's cat is petrified, Hermione says, "The Chamber of Secrets has been opened. Enemies of the heir beware. It's written in blood." Two things: Hermione is rarely wrong and the writers needed the audience to know the messages were written in blood. In the movie there is no mention of paint.
This is your basic answer according to movie canon. It was written in blood; it doesn't say what kind or from whom/what the blood is coming from.
A couple other tidbits from the movie Chamber of Secrets that might be relevant:
In a deleted scene¹, Hagrid meets up with Harry after Harry overhears the Hufflepuffs discussing him as being the Heir of Slytherin in study hall. Hagrid is holding a dead chicken; Harry asks what's going on and Hagrid gestures with the chicken and says (paraphrase), "Second one killed this term. Figure it's got to be a fox or a Bogalug Bear, so I thought I'd ask Professor Dumbledore if I could put a little charm around the hen coop."
In the movie, when Harry and Tom Riddle are facing off in the Chamber of Secrets, Tom Riddle says, "It was Ginny who wrote the threatening messages on the wall." He doesn't address the dead chickens or what kind of blood the messages were wrote in. Nor does he address feathers.
So, it's blood. We don't know what kind. However, I don't think it's much of a stretch, based on the movie facts only, to assume Ginny wrote the messages in chicken's blood. In the movie.
¹My copy of Chamber of Secrets is the Ultimate Edition, which comes with both the theatrical and extended versions of the film.