65 ILCS 5/11-85-4
A municipality participating in the construction of an improvement specified in this Division 85 has jurisdiction over the part thereof lying within the corporate limits of the municipality. The participating township has jurisdiction over that part of the improvement lying outside the municipality and within the township. The municipality and the township may repair, maintain, or reconstruct the portions of the improvement within their respective jurisdictions in the manner provided by law in cases of similar improvements lying wholly within their respective jurisdictions. But nothing contained in this section affects any power otherwise given by law to either the municipality or the township to expend money in the repair, maintenance, or reconstruction of the entire improvement or any part thereof.
Although parts of the improvements are under separate jurisdictions, the municipality and the township interested may enter into contracts with each other providing for the repair, maintenance, and upkeep, including lighting, of the improvement, apportioning the cost thereof and providing the method of that repair, maintenance, and upkeep, as may be agreed upon between them.
A township may surrender its jurisdiction over such an improvement to the municipality jointly interested, by agreement made between the corporate authorities of both the municipality and the township. The municipality thus assuming that jurisdiction thereafter shall be chargeable with the repair, maintenance, and upkeep of the part of the improvement so turned over, and may exercise its police powers thereover in like manner as if the improvement lay entirely within the municipality.
65 ILCS 5/11-85-4