Ceiling Water Damage Question

Hello, hoping someone can help me.

In my current rent while taking a bath water displaced into the overflow pipe and somehow caused damage to the ceiling below. The bath was never left alone and water never came over the side of the bath, only a small amount into the overflow pipe when getting in the bath. It seems as though the overflow is either not plumbed in correctly or not sealed correctly. Who would normally be liable for this?

Thanks