The evidence that Ezekiel Cheever uses to justify the arrest of Elizabeth Proctor is the doll that he finds at her house.
When he finds the doll, he also finds that there is a long needle stuck into its stomach. This needle is important because Abigail has accused Elizabeth Proctor's spirit of stabbing her while she ate at Parris' house.
When Elizabeth is taken away, John Proctor asks Mary Warren to admit to the fact that it was she who made the doll. She refuses, telling Proctor that if she does, Abigail will reveal their adulterous affair.
Abigail has provided testimony that Elizabeth Proctor sent out her specter, or spirit, and that it pushed a long needle into her belly while she sat at dinner. Spectral evidence was permitted during the Salem Witch Trials in 1692, and many believed that a witch could send out either her own spirit or the spirit of her animal familiar (like a cat or bird) to pester or torture an innocent accuser. Only the accuser, then, and the witch could see the specter and provide testimony, but since the witch would never accuse herself, only the word of the accused could be trusted in the eyes of the court. Obviously, this kind of evidence is quite easy to fabricate since there is no way to verify its truthfulness; however, it was permitted in court nonetheless.
Toward the end of Act Two, Mary Warren does admit that she pushed the needle into the poppet herself, for safekeeping, and that Abigail saw her do it in court that day (though she does not realize, yet, that she is giving evidence against Abigail). Elizabeth, realizing how Abigail has framed her becomes angry and says, "The girl is murder! She must be ripped out of the world!" Cheever takes this statement as further evidence that Elizabeth wants Abigail dead. When Proctor tells Mary that she will have to go to the court and repeat what she's said, she refuses because she knows that the girls will turn on her too.