There are both potential Unrelated Business Income Tax (UBIT) and local property tax concerns. First, tax exempt organizations generally do not need to report rental income as unrelated business income (UBI) unless it is financed with tax exempt debt instruments. "Rents from real property, including elevators and escalators, are excluded in computing unrelated business taxable income. Rents from personal property are not excluded" (IRS Publication 598).
"Investment income that would otherwise be excluded from an exempt organization's unrelated business taxable income must be included to the extent it is derived from debt-financed property. The amount of income included is proportionate to the debt on the property."