The two sides are millions of dollars apart on what they state would pay the city toward future road maintenance and that negotiations have been put on hold, Goodnight told the Kokomo Tribune.
"There wasn't any money for salt or general maintenance," he said. "We couldn't reach a conclusion, so it's the state's responsibility."
Highway department spokesman Harry McGinity said the agency is properly clearing and maintaining Indiana 931 through the winter.
"The negotiations are at a standstill and the parties are far apart in their negotiations," he said. "INDOT is looking forward to maintaining and planning to maintain that stretch of road for the foreseeable future."
The new U.S. 31 bypass around Kokomo's east side opened in November, allowing travelers to avoid 15 traffic lights through the city about 40 miles north of Indianapolis.
The Kokomo bypass is part of a $1.2 billion reconstruction project for U.S. 31 linking Indianapolis and South Bend. Other major parts include roadway sections being built in the northern suburbs of Indianapolis and between South Bend and Plymouth.
Local governments have taken over other sections of former state highways under agreements such as a 2012 deal under which the highway agency paid nearly $23 million to Lafayette for it to take over a section of U.S. 52.
Greg Walls, manager of Indy Tire and Auto Service along Indiana 931 in Kokomo, said it has taken longer for snow to be cleared from the road this winter while problems with potholes persist.
"We're kind of seeing late snow removal," he said. "Last week during the last storm, the intersections weren't clear all day. They push through and cleared the main stretch, but just getting across those intersections was difficult."