(1) When a municipality levies a tax under this Article, which municipality is situated wholly or partly in a township which also levies a tax under this Article, the levy and collection of the library taxes are subject to these provisions: (a) If a city, village or incorporated town which levies a tax under this Article is located in a county of less than 1,000,000 inhabitants and is situated wholly or partly in a township which levies a tax under this Article, such township may proceed as follows unless the authority to levy a library tax in the area which lies in both the municipality and the township has been determined under subsection (c). The township may cause an abatement in full of the township library tax on property subject to such tax as also lies within a city, village or incorporated town which also levies a library tax for the same year. However, such township may instead pay to such city, village or incorporated town the entire amount collected for such township from taxes levied under this Article on property subject to a tax which such city, village or incorporated town levies under this Article.
     Whenever any city, village or incorporated town receives any payments from a township as provided in this Section, such city, village or incorporated town shall reduce and abate from the tax levied by the authority of this Article a rate which would produce an amount equal to the amount received from such township.
     (b) If a city, village or incorporated town which levies a tax under this Article is located in a county of 1,000,000 or more inhabitants and is situated wholly or partly in a township which levies a tax under this Article, such township shall proceed as follows unless the authority to levy a library tax in the area which lies in both the municipality and the township has been determined under subsection (c). The township shall cause an abatement in full of the township library tax on property subject to such tax as also lies within a city, village or incorporated town which also levies a library tax for the same year. However, such city, village, or incorporated town shall, upon collection of its library tax on such property, pay 1/2 of the collections to the township for library purposes.
     (c) If any part of a city, village or incorporated town which levies a tax under this Article is situated within a township which levies a tax under this Article, the corporate authorities of the municipality or township may cause the question of which such tax shall be applicable in that area which is situated in both the municipality and township to be submitted to the electors of such area at any regular election. The question shall be certified to the proper election officials, who shall submit the question at an election in accordance with the general election law. The question shall be in substantially the following form:
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    Shall the area which lies in both (insert name
of municipality) and (insert name of township) be
subject to taxation for library purposes by (insert
name of municipality) or by (insert name of township)?
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    By (insert name of municipality)
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    By (insert name of township)
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     After such election, library taxes under this Article shall be levied and collected in such area only by the governmental unit which received the larger number of votes cast in such election.
     (2) If a city, village, incorporated town or township which levies a tax under this Article is situated wholly or partly in a library district which levies a tax under “The Illinois Public Library District Act”, such city, village, incorporated town or township shall pay to such library district the entire amount collected for such entity from library taxes levied under this Article upon taxable property within such library district.
     Whenever any library district receives any payments from any city, village, incorporated town or township as provided in this Section, such library district shall reduce and abate from the library tax levied by the authority of “The Illinois Public Library District Act” on property which is subject to taxation for library purposes by both the district and the municipality or township a rate which would produce an amount equal to the amount received by such library district.