Tituba is a static character. The most important elements of her character are functionally oriented, used to help communicate certain aspects of the Salem community and to demonstrate a moral relativity regarding witchcraft. These elements are not changing and are intended to be seen as permanent differences between Tituba and the community of Salem.
Tituba is expressive of a view of witchcraft that is quite different from the view commonly held in Salem.
She is suspected of black magic due to the traditions of Voodoo that were prevalent in her home country.
She is also an outsider, seen by Parris and others as a threat to the unity of Salem. This unity is the community's greatest tool for survival and Tituba, with her foreign belief system, is a threat to this unity.
These aspects of Tituba's character do not change and they are, effectively, the only important elements of her character.
Though Tituba does appear in the last act of the play and appears rather hysterical, this is not a significant change in her personality. She begins the play on the verge of hysterics, worried that she will be put to death for her role in the midnight activities discussed in the play's opening scene.
Think about the definition of each. A dynamic character needs to somehow CHANGE throughout the course of the story. A static character remains the same. Miller does not go into a lot of depth with the character of Tituba. Throughout the play, she remains an uneducated, unknowing scapegoat for the girls.