Property owned by, or being acquired pursuant to, an installment purchase agreement by a county, township, city, village, or school district used for public purposes and property owned or being acquired by an agency, authority, instrumentality, nonprofit corporation, commission, or other separate legal entity comprised solely of, or which is wholly owned by, or whose members consist solely of a political subdivision, a combination of political subdivisions, or a combination of political subdivisions and the state and is used to carry out a public purpose itself or on behalf of a political subdivision or a combination is exempt from taxation under this act. Parks shall be open to the public generally. This exemption shall not apply to property acquired after July 19, 1966, unless a deed or other memorandum of conveyance is recorded in the county where the property is located before December 31 of the year of acquisition, or the local assessing officer is notified by registered mail of the acquisition before December 31 of the year of acquisition.