It was opened by DA councillor Goodman Madondo and implicates several senior managers in the alleged over payment.
Hawks provincial spokesperson Simphiwe Mhlongo confirmed that a case had been opened but could not go into details.
He said the case had been recently transferred to the Hawks from the Richmond police station.
Madondo said the payment was one of several that have raised red flags and, consequently, they would be demanding that all payments made after the death of the then municipal manager, Sibusiso Sithole, be investigated.
Sithole was gunned down in Richmond last year, a few days before he was due to leave that job.
At the centre of the criminal case are allegations that senior staff members in the council had authorised that a contractor be overpaid by more than R700 000.
“The contractor of one of the major infrastructure projects in the area had sent an invoice of R272000, but these managers authorised that the contractor be paid R1 million,” said Madondo.
He said the invoice was processed on April 25, 2017.
Three senior managers are fingered in the payment. Attempts to reach some of the officials named were unsuccessful.
Municipal spokesperson Sibonelo Bhengu said they could not speak in detail as it was a police matter.
“However, we believe the councillor should have first tabled the matter at the council before taking it to the police, so he could have clarity on the allegations he is making. We believe he has incomplete information. We will now wait to present such information to the relevant authorities,” he said.