As stated by Jontia, yes, Nina is a mutant.
While this is never explicitly states it seems clear enough from the film that she has the ability to communicate and control animals. She calls upon a flock of birds to attack the police officers before she is killed.
Police Officer: What's happening? She is one of them.
Police Officer: Make her stop.
Erik: She can't control them.
Erik: She's frightened.
Nina: I'm not letting them take you! I'm not letting them take you!
Police Officer: Make it stop!
Erik: No. No, Nina! . Nina? Nina. No. Don't... Please. Please. Please. What have you done? Not my babies. Not my babies. IS THIS WHAT YOU WANT FROM ME? Is this what I am? Is this what I am
The police clearly point out that the animals seem to be attacking them based on Nina's command. And while Erik's first defence is that it's not her, in desperation he clarifies that due to her fear she is unaware that she is controlling them and that she can't do anything to help it.
The clip can be found below. However, there are no subtitles to the polish, unfortunately... I will work on this when I get time. The scene still clearly portrays Nina's powers manipulating the birds to attack the officers.