Pilot David Traill, two other crew members and seven bar customers died when the aircraft crashed in Glasgow on November 29 2013.
Constable Niall McLaren from the Police Air Support Unit spoke of his time as an air observer from 2007 until June last year.
Donald Findlay QC, representing the family of one of the seven people killed inside the Clutha, said: “One would therefore assume you had flown with Captain Traill on some occasions.”
Mr McLaren replied he had.
Mr Findlay then asked if Mr Traill had been a “stickler for procedure”.
He said: “Yes.”
Mr Findlay added: “You would not expect him to be gung-ho or ignore warnings?”
Mr McLaren replied: “Not at all.”
The inquiry has previously established a number of low fuel warnings were highlighted in the helicopter during its flight from Bothwell in South Lanarkshire back to base in Glasgow.
Mr McLaren said he had only ever encountered such a warning once before and it was “30 seconds before landing”, with procedure dictating a 10-minute window for a pilot to land after such a warning.
Transcripts of Mr Traill’s two conversations with an air traffic controller at Glasgow Airport were also shown at the inquiry.
Air traffic controller Andrew Campbell began his shift shortly before 10pm on November 29 and was informed the helicopter was due to leave Edinburgh airspace and contact again on approach to Glasgow.
He recalled the first contact was at around 10.05pm when Mr Traill asked for visual flight rules (VFR) for Bothwell before recovery - when the aircraft lands at base.
Mr Campbell said he gave the standard clearance and it was acknowledged by the pilot.
Gordon Lamont, advocate for the Crown, asked if “there were any concerns about the flight”.
Mr Campbell said: “None at all.”
Mr Lamont added: “Was there anything in his voice or tone or concerns raised by discussions?”
Again, he replied: “None at all.”
“No audible gong or warning in the background?”
Mr Campbell said: “No.”
When asked to describe the call, the air traffic controller called it “totally standard” and it “didn’t feel any different”.
In regard to dealing with the police vehicle, Mr Campbell said: “We’re taught to be discreet, people could be listening on the ground, we try not to bother them as much as possible.”
Clearance was given to the aircraft and Mr Lamont asked the same questions for the second call, which came from Mr Trail at 10.18pm with an approach complete message.
Again Mr Campbell replied there were no concerns, nothing noticeable in his tone of voice and no audible gongs or mayday message in the background.
When asked about when he knew of the crash, Mr Campbell said: “Ten to 15 minutes after I thought it landed, I got a call from Prestwick (air traffic control) asking if I knew anything of a helicopter crash over Glasgow city centre.”
Mr Lamont suggested it “might seem strange (he) didn’t know”.
He replied the helicopter would have gone off radar when it approached around 200ft as it would have been on course to land at the base, hence his assumption it had landed.
The inquiry before Sheriff Principal Craig Turnbull continues at Hampden Park.