If you hadn't posted this on an internet forum, your brother could have just given the gun to your father. Nobody cares.
But since its been posted, you now have to follow the letter of the law perfectly. That means your brother needs to go to a FFL in CT and transfer the gun to him. Then the FFL will do the transfer to your father. There is no gun registration in CT. They do record transfers, but they do not track what gun is owned by whom. Rather, they track who owns what guns. There is a big difference.
Since there is no requirement to report out of state sales, a gun could be associated with multiple people. If they tracked what gun is owned by whom, it is possible that a gun could be sold out of state through an out of state FFL, with no record of the transfer made to CT. Then if it was sold back into CT and transferred by a FFL, it would then be associated with two people. The system can't handle that. So its just a simple list next to your name.
Either way. Don't sweat the small stuf. The DPS is completely uninterested in hassling people re transfers between fathers and sons. Its the least of their worries.
Don