In present perfect the verb agrees with the direct object if it is placed before the verb. So "They have recognized the girl" would be "Hanno riconosciuto la ragazza", but "Mi hanno riconosciuta" if the speaker is female. It is the same rule as in French.
It is up to you, and it is in the DL tips:
If the verb is conjugated with any other direct object clitic, it can OPTIONALLY match its gender and number:
Antonio mi ha chiamata. OR Antonio mi ha chiamato. Antonio called me. (For a feminine "me.")