A mysterious push to merge three neighboring towns with Naperville has taken a step forward and could appear as a referendum question on the April 4 ballot.

Petitions to put the annexation question before voters in Lisle, Warrenville, Woodridge and Naperville were filed Tuesday in DuPage County’s 18th Judicial Court and Will County’s 16th Judicial Court.

The referendum in each town would ask a basic yes or no question. In Woodridge, for example, it would ask voters “Shall the Village of Woodridge be annexed into the City of Naperville?”

Although no signatures on petitions were gathered in Naperville, Mayor Steve Chirico said it’s his understanding the question also would appear on the ballot in his city.

Officials in all four municipalities said the chances of actually merging the towns are remote and any such effort would be enormously complicated, adversely affect other taxing bodies such as park and library districts, and raise countless other issues.

They also are questioning who’s behind the merger idea and why.

“I see nothing positive about this,” Warrenville Mayor David Brummel said Thursday. “It’s a huge waste of time and resources.”

Brummel, Chirico and Lisle Mayor Joe Broda said officials in their cities are studying the petitions and looking for potential flaws that would allow them to try to scuttle efforts to put the question on the ballot. Brummel said the towns have until early next week to file such objections, although there’s some confusion as to the actual deadline.

“We’re looking to see if there is a legitimate challenge,” he said.

Jack Knight, assistant to the village administrator in Woodridge, said his town is sending out a note on its social media accounts that says, in part, “These petitions were not initiated by Woodridge, Lisle, Warrenville, or Naperville, nor have any of their respective elected bodies endorsed any such action.”

Broda said officials in his town are uncertain whether there are enough legitimate signatures to put the questions on the ballot.

“We’re looking at the credibility of the whole thing,” he said. “How can petitions be filed by people from outside the county with the circuit court?”

He said there’s also confusion about whether the questions would be binding or advisory, and what would happen if the questions remained on the ballot in some of the towns but not others.