"Would you please send a copy to Mark and a copy to me."
The personal pronoun is governed by the preposition 'to', so must be the objective case of "I", that is, "me".
As you can see, the sentence ends in "me".
A sentence can end in "I" :
In some melodrama, one character might exclaim, "None other than I! Many years have I kept my real identity a secret, waiting for the moment to avenge...".
The first sentence ends in "I"