Dennis et al If the circuit is to be split into two separate circuits, without two or more ungrounded current carrying conductors terminating on the same yoke or strap, and the installation is governed by the US National Electric Code (NEC), then there is no requirement to use a two pole breaker unless the circuit will supply 240 volt loads.
Some will argue very forcefully that it is good practice but I disagree. A double pole breaker will open both circuits on a fault or overload thus plunging the entire building served into darkness because a saw hung up in a piece of paneling for instance.
Separate buildings always need a building disconnecting means. On residential property this can take the form of a common snap switch or set of three way switches in each ungrounded conductor. Better practice is to use a double pole switch that will open both ungrounded conductors simultaneously. Best practice would be to use a disconnect that is listed for use service equipment which would be required if it were not residential property.