The fire truck involved in the deadly LaGuardia Airport plane crash was not equipped with a key device to track its movements around the runway — and it’s unclear if the driver could even hear the air tower’s desperate pleas to stop, NTSB officials said Tuesday.

The alarming details were revealed by National Transportation Safety Board Chairwoman Jennifer Homendy — who added that the agency still doesn’t even know which air-traffic controller was in charge of ground activity at the New York City airport at the time.

“It is not clear who was conducting the duties of the ground controller,” Homendy told reporters, detailing investigators’ early findings about the crash late Sunday.

“We have conflicting information. We have some information it was the controller-in-charge. We have some information it was the local controller.”

The confusion over what happened in Laguardia’s tower late as the jet began its descent extended to what happened on the ground itself, Homendy said.

She noted that the fire truck also did not have a transponder — a crucial piece of equipment that would give air-traffic controllers a clear picture where it was on LaGuardia’s runways.

“Should they have transponders? Yeah, they should,’’ she said.

“Air-traffic controllers should know what’s in, you know before them. Whether it’s on airport surface or in the airspace. They should have that information to ensure safety.”

A federal probe into the accident was launched after Air Canada Flt. 8646, which departed from from Montreal, t-boned a Port Authority Police Aircraft Rescue Fire Truck as it landed at LaGuardia.

The harrowing, caught-on-video crash obliterated the front of the CRJ-900 jet – killing young pilots Antoine Forest and Mackenzie Gunther and injuring 41 people, including the two Port Authority officers in the truck.

Audio released after the crash apparently revealed that the jet had received the go-ahead to land on LaGuardia’s Runway 4 — at the same time the Port Authority truck was cleared to drive on the same runway while responding to a separate emergency on a United Airlines plane.

Homendy said two air-traffic controllers were working in the tower when the collision unfolded.

The controller-in-charge’s duties included overseeing “clearance delivery positions,” which provides pilots with departure clearance, the chief said.

But who was meanwhile also handling activity on the ground remained unclear, Homendy said, noting it’s not uncommon for airports to give controllers double-duty on less-busy late shifts – despite the feds’ long-standing concerns about the practice.

“We have seen different information about how many certified professional controllers were in the facility,” she said.

“We need to verify that starting with interviews this afternoon. We will interview the local controller at 4 o’clock this afternoon. We do have logs, but there is also conflicting information including dates and times on the logs. So, now we have to go through that and rectify some of those inconsistencies.”

After the crash, at least one of the involved air-traffic controllers remained on duty for several minutes — a departure from normal practice, Homendy said.

“Normally, they would have been relieved,” she said.

“We have questions about that. Was anybody available to relieve that controller? We don’t know that yet.”

Investigators’ early uncertainty over what happened in LaGuardia’s tower before and after the collision was matched by a lack of information from the ground, Homendy said.

She noted that the Port Authority fire truck did not have a tracking transponder.

The transponder could have helped trigger the LaGuardia’s runway safety system known as ASDE-X about a potential collision, she said.

Without transponder data from the fire truck, the ASDE-X system didn’t throw up an alert, the NTSB chief said.

Audio revealed a air-traffic controller desperately — and repeatedly — pleaded for the truck to “stop” mere seconds before the collision, but Homendy said it’s uncertain whether the two Port Authority firefighters aboard even heard the last-ditch attempt to halt the impending disaster.

“We don’t know that yet, we need to do interviews of those two firefighters,” she said.

A Port Authority rep declined to comment on The Post’s queries.

“This is an active NTSB investigation, and as with any ongoing investigation, we’re not able to comment on specifics,” the representative said in a statement. “Our focus is on ensuring investigators have full access and support as they carry out a thorough and independent review.”

Homendy cautioned against reports contending that distraction by the air-traffic controllers could have played a role in the crash.

“We rarely, if ever, investigate a major accident where it was one failure,” she said.