Operator Bond grounded its fleet of EC135 helicopters yesterday as a precaution while the issue, discovered on an air ambulance in the north west of England, was examined.
The Association Of Air Ambulances, which represents the majority of the air ambulance network, said 16 of its 36 helicopters in the UK were affected by the grounding.
Police Scotland said its helicopter had been cleared to fly.
A spokeswoman said: "The restrictions placed by Bond on the Police Scotland helicopter have been lifted. The Police Scotland Air Support Unit is now fully operational."
An initial report from the Air Accidents Investigation Branch into the helicopter involved in the Clutha tragedy said there was "no evidence of major mechanical disruption of either engine" of the helicopter as it returned from an operation in Dalkeith, Midlothian.
Bond Air Services said: "As a precautionary measure, following an issue with the fuel indication system on one of our aircraft yesterday we temporarily suspended service operations whilst we undertook further technical investigations of our fleet of EC135s."
Eurocopter, the aircraft manufacturer, said the grounding did not apply to the rest of the EC135 fleet.