The accusation comes after the Convention Of Scottish Local Authorities, the umbrella body for councils, wrote to its members questioning information about the ballot provided by teaching unions.
Teachers are being offered pay increases of 1% this year and 1% next year, but the deal will only go ahead if they vote in favour of separate changes to their conditions.
Moves to improve the pay for supply staff - whose payments have been cut, leading to staff shortages - will also only go ahead if the changes to working conditions are accepted. The ballot closes on October 21.
In its letter to councils, Cosla said that "regrettably" the Educational Institute of Scotland (EIS) teaching union had "left out some essential detail to inform its members of the implications of their vote".
It said: "The danger is the EIS has muddied the waters and failed to clearly advise its members that their pay award .... is contingent on a yes vote.
"It is crucially important the teaching workforce has the full information available when participating in the ballot."
However, Larry Flanagan, EIS general secretary, accused Cosla of "impertinence".
He said: "The EIS has always been committed to a ballot of members on these proposals, as the management side is well aware.
"The EIS was very clear - in the ballot materials sent to members, on the EIS website, and in materials sent to schools - of the likely implications for the pay offer should members choose to reject the current ballot."
A Cosla spokesman said: "We, as employers, thought the EIS ballot material was misleading and did not make it sufficiently clear the vote was also a vote for the pay deal. We felt we had a responsibility to our employees to provide clarity."