In The Crucible, what did Mary Warren have to do with accusing of Goody Osburn?
Note: This answer pertains to the screenplay for the movie of Arthur Miller's play The Crucible. The screenplay was also written by Arthur Miller.
Mary Warren, as "an official of the court," is there every day during the proceedings, and so she was present when Goody Osburn was brought in and questioned. The first time Goody Osburn was accused was at Reverend Parris's house when Tituba, to get out of being hanged or whipped, claimed she saw Goody Osburn with the devil. While Osburn is being questioned in the courts, Mary states that, "I feel a misty coldness climbin' up my back, and the skin on my skull begin to creep, and I feel a clamp around my neck and I cannot breathe air; and then-I hear a voice, a screamin' voice, and it were my voice-and all at once I remembered everything she done to me!" Mary goes on to explain that once when she turned Osburn away from the door without food, Osburn mumbled and she "thought [her] guts would burst for two days after." The implication is that Osburn mumbled some sort of curse or witchcraft to make Mary sick. When asked to repeat what she mumbled, Osburn claimed it was her commandments, but then couldn't repeat them, and so Mary says that "they had her in a flat lie!"
So, although Osburn was not there on Mary's accusation, she is the one that brings forth the damning evidence that "proves" Osburn is a witch, at least in the eyes of the court.
In Arthur Miller's play version of The Crucible, the story Mary tells Elizabeth Proctor in Act Two about the woman in church who cursed her and made her very sick for two days is actually about Sarah Good, not Sarah Osburn. Mary says that Judge Hathorne questioned Goody Good, saying, "'Sarah Good, [...] what curse do you mumble that this girl must fall sick after turning you away?'" Sarah Good lied and said that she only recited the commandments, but when she could not recite any of them in court, it was seen as evidence of her guilt. Sarah Good later makes a confession of her guilt, and so she will spend some time in jail.
In the play The Crucible, as far as Sarah Osburn, Mary only says that she would not confess and so she "will hang!" Tituba initially accused Goody Osburn of witchcraft at the end of Act One, and then Abigail picked up the chant and accused Osburn as well. Tituba probably accused Good and Osburn first because she knew people would believe they were witches (just as Abigail seemed to know that no one would have trouble believing that Tituba was a witch). In Act Two, Elizabeth says that Goody Osburn is "drunk and half-witted," and this is probably what made her an easy target for accusations. Therefore, Mary really has little or nothing to do with the conviction of Osburn, at least not that gets reported to us.