"turn the matter" is a correct and usable phrase in written English.
You can use it as a way to say that something has been rethought, changed, or reversed in decision or opinion. Example: After careful consideration, we have decided to turn the matter and allow members to vote by mail in the upcoming election.
If not, better to avoid persistent complaints and turn the matter over to Sergeant Friday.
The Senate encouraged the trend by rejecting higher mileage standards for automobiles and voting to turn the matter over to the Bush team.
I resist the idea of expecting music to feed or prompt an emotional state, so I tried to turn the matter on its head.
Mr. Specter says he is sympathetic to the administration's concern that briefing lawmakers could lead to leaks, which is why he wants to turn the matter over to the courts.
A high-level official of the agency confirmed the staff members' desire to turn the matter over to the Justice Department, but said no official decision had been made.
But they said that a decision was likely to be made fairly soon, and that it was also possible that Ms. White's office might turn the matter over to yet another set of federal prosecutors to conclude.
Krislov says that he turned the matter back to the kids.
The attorney general at the time, Andrew M. Cuomo, who succeeded Mr. Paterson as governor, turned the matter over to Ms. Kaye.
C.I.A. officials referred the breach to the Justice Department, which eventually turned the matter over to Patrick J. Fitzgerald, the special counsel.
But a "Don Giovanni" lacked character, as if he had simply turned the matter over to the musicians of the Vienna Philharmonic.
When another complaint was filed a year later, Hirsch turned the matter over to Joseph P. Marshall, who had the title of facilities manager.
