Answer: C. Objective
Explanation: The whole complement of this sentence ("between Sheila and her/him/them/me/you") is a prepositional phrase led by the preposition between, and as a general rule, personal pronouns always take their object form when following a preposition. Nominative and possessive pronouns, then, have no place in this part of the sentence, and the antecedent of a pronoun is just the noun that is being replaced by it.