The police doesn't have much of discretion on the subject according to common training material. Consider the following points selected from Stop Violence Against Women website[1]:

  To determine the predominant aggressor, police must consider:
    The seriousness of injuries received by each party
    The height and weight of the parties
    Which party has the potential to seriously injure the other party
    Orders for protection that have been filed by a party
    Whether a party has a fearful demeanor
    Whether a party has a controlling demeanor

-- [1] http://www.stopvaw.org/determining_the_predominant_aggressor