My rental house was broken into. Who is responsible for repairs to broken door?

I am not from your state but generally speaking it would be the landlord's responsiblity since it is not within the unit itself. If you can prove that it was done by a tenant or their guest then you could most likely charge them for it. Good Luck.

Agreed with the previous answer that the landlord is usually responsible for structural damage or damage to the house itself rather than to the property within it. Also, just because the tenant did not file a police report doesn't mean that the landlord can't. The property belongs to the landlord and thus the landlord is also a victim.

You should file a police report regarding the damage and then you, as the landlord, will be responsible for the damage unless you can show that the tenant was involved somehow. You will in turn be considered the victim and eligible for restitution in any criminal damage or burglary case, if one is ever filed. It is odd to me that the tenant did not file a police report, which is what makes me encourage you to file the report so that the police will most likely interview the tenant and determine whether they think this truly was an independent criminal act or whether the tenant or someone the tenant knows was involved. You should then also consider whether your insurance will cover the damages, or whether the damages are below the threshold of your deductible. If the pattern repeats itself, you may be able to take additional action. For example, I had a tenant that "mysteriously" had her front door damaged repeatedly and she was never sure how it happened. It turned out to be her abusive ex-boyfriend.