In his plea, Singh had contended that since Enforcement Directorate had after a probe found that the allegations against him were baseless, all proceedings against him should be quashed.
Rejecting his plea, a three judge bench comprising acting Chief Justice A Lala, Justice S K Gupta and Justice P K S Baghel directed the state government for nominating an agency to investigate the matter.
The court, however, said no useful purpose would be served by regularly monitoring of the matter by the court.
The petitioner Shivakant Tripathi had sought a probe by a Special Investigation Team and its monitoring by the court.
The allegation in the petition was that Singh had misappropriated crores of rupees when he was functioning has Chairman of UP State Development Council.