Agreeing with @Carl, I wonder what you mean by co-own. Does the property belong to your parents and you were gifted or expect to be the beneficiary at their passing or what? Whereas these do not make a difference in India, if you are a US resident, the type of ownership or transfer may make a huge difference when you dispose off the property.
Note also that as a second home , while property taxes and mortgage interest paid by you may be deductible , nothing else is. Also to the extent that you are personally liable for these amounts and that you actually pay, are deductible ONLY when itemized and under the current limitations).
Are you a resident or resident for tax purposes or a visitor in the USA -- what visa or is it Green Card?
Namaste ji
