If my apartment caught fire due to the improper installation of an A/C unit, can I sue the responsible party?
I don't have renters insurance.
If you suffered damages (loss of clothing, appliances and having to get another apartment costing more per month than what you were paying) and if the improper installation by a third person (not you) of the air conditioning unit caused the fire and your damages, you have a case to sue.
Does your landlord have an insurance policy that possibly covers your belongings under it?
Does the person who installed the air conditioning unit improperly have insurance? If so, you need to make a claim to that insurance policy for your damages. Make sure you have photographs and receipts to show what was damaged and the initial cost of the damaged item.