Two men aged 25 and 34 were detained in the city on Monday.
A third man aged 41 was arrested in west Belfast on Tuesday night.
All three have been released unconditionally by police.
A booby trap bomb was found under the family car of the off-duty police officer on Sunday afternoon.
The PSNI officer, his wife and two young children were about to leave their Upper Newtownards Road home for lunch when he spotted the device.
Dissident republicans are being blamed for the attack.