Scripture is somewhat ambiguous, and taken at face value, it looks like both just dropped dead. But Holy Tradition, being more than just Scripture, seems to indicate that Saint Peter executed judgement (to me at least, correct me if I err).
Rejoice, thou who didst sternly punish the sacrilege of Ananias with death;
Rejoice, thou who didst likewise commit Sapphira, who was guilty of that sin, to the same punishment!
-Ikov VII from the Akathist to Saints Peter and Paul
And Peter too wrought a twofold slaughter, nevertheless what he did was of the Spirit.
-Saint John Chrysostom, Homilies on Matthew (note this is explicitly in the context of whether killing is ever appropriate).
Peter all but pleads for himself, when at the point to inflict the punishment, and at the same time gives a lesson to the rest. For because the act would seem exceeding stern, therefore it is that he does so much in the case.
-Saint John Chrysostom, Homilies on Acts
Rejoice, thou who didst sternly punish the sacrilege of Ananias with death;
Rejoice, thou who didst likewise commit Sapphira, who was guilty of that sin, to the same punishment!
-Ikov VII from the Akathist to Saints Peter and Paul
And Peter too wrought a twofold slaughter, nevertheless what he did was of the Spirit.
-Saint John Chrysostom, Homilies on Matthew (note this is explicitly in the context of whether killing is ever appropriate).
Peter all but pleads for himself, when at the point to inflict the punishment, and at the same time gives a lesson to the rest. For because the act would seem exceeding stern, therefore it is that he does so much in the case.
-Saint John Chrysostom, Homilies on Acts