It might, but it depends on the situation and what the various insurance policies for the condominium building and units cover. The condo association's "master policy" typically covers common areas and building exteriors, but it might cover a portion of the space between your unit and your neighbor's condominium.
Your condo home insurance policy covers damage to your unit and provides liability protection if people are injured on your property or you cause damage to others.
Your downstairs neighbor's policy would cover damage to his unit. In this case, he most likely would file a claim with his home insurance company. But if the insurer determined it was your fault that the tub overflowed, then it would go after your home insurance company to pay for a portion of the repairs (or all the damage) and for your neighbor's deductible. Your insurer then would make payment under the liability portion of your condo insurance policy--unless it discovered you let the tub overflow on purpose to damage the neighbor's property. The insurance companies would also check whether the condo association's master policy should pay for any portion of the repairs.
Call your home insurance agent to get information on how to proceed, and provide your insurance information to your neighbor.
For more, see "Condo insurance: How much is enough?"
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