Yes, you will not be taxed in PA on the gains from the sale of the property. Actually, only Illinois should receive tax for Illinois rental income and sale.
Pennsylvania instructions apply to income from Pennsylvania sources. See below for a further analysis.
For your reference:
2019 New York Part-Year and Nonresident Instructions
2019 Illinois Nonresident Instructions
2019 Pennsylvania Part-Year and Nonresident Instructions (see page 6 regarding school district code and begin with instructions on page 43)
2019 Pennsylvania Schedule NRH Form and Instructions
Pennsylvania Nonresidents and Part-Year Residents:
Part-Year Residents of Pennsylvania. Part-year residents are subject to PA personal income tax on all income earned, received and realized from all sources when residents of PA. Part-year residents are also subject to PA tax on income earned, received and realized from sources within PA when they were not a PA residents. Part-year residents are not subject to PA tax on ordinary interest, dividends, gains, intangible property or gambling and lottery winnings from PA sources while a nonresident. Some exceptions apply; see below for additional detail.
Apportioning Income (Loss) on PA Schedule NRH
As a nonresident, you may apportion income earned within and outside PA. Apportion PA-taxable compensation when your employer does not separately report PA wages on Form W-2. You must apportion income (loss) from operating a business within and outside Pennsylvania unless you maintain books and records that clearly substantiate and separately allocate your PA-source receipts, expenses, liabilities, etc.
