Operation Encompass, a South Yorkshire Police initiative, sees schools given warnings by officers who have attended domestic violence calls where school-age children were present.
The scheme, which Sheffield, Rotherham and Doncaster councils have already signed up to, is intended to reduce the impact of early exposure to domestic violence - known to cause problems in later life.
But council bosses have declined to take on the scheme after initial talks.
Coun Margate Bruff, cabinet spokesman for children’s services, said: “As a council we have taken the decision not to proceed with Operation Encompass.
“We will still receive all domestic abuse notifications and screen them all.
“Any that we believe meet the threshold for a statutory assessment by Children’s Social Care will receive an assessment by this service.
“During our assessments, we consult with schools as a matter of course, although under ‘child in need procedures’, this should still be with parental consent. All children will be safeguarded.”
At 7.30am every day, school staff in areas utilising Operation Encompass are given automatic reports of domestic violence incidents where school age children were found.
Those children can then be supported and monitored as part of a developing system of dealing with domestic violence, with arrest rates on the rise in South Yorkshire.
The scheme is launched this month following a report presented to police and crime commissioner Dr Alan Billings.
Assistant Chief Constable Tim Forber told a meeting of Dr Billings’ Public Accountability Panel, attended by the Local Democracy Reporting Service: “Children who suffer an early childhood experience (of domestic abuse) are far more likely to have poor outcomes and have an entry at some point into the criminal justice system..”