If a drainpipe blockage is a result of fair wear and tear (e.g. tree roots) the property manager/owner is responsible for ensuring the drainpipes are returned, and maintained, to a working standard.
If the tenant has caused the blockage (e.g. a child puts a toy down the drain) they may be responsible for the removal of any items that caused the problem. The tenant may also have to pay for the cost of removal and any damage.
However, if the tenant has not done anything to block the gutters, the property manager/owner may be responsible for cleaning them.