The unidentified police officer took multitasking to a whole new level Sunday as he borrowed a lighter from another nearby officer to ignite his stogie while straddling a man on the ground whom he was placing under arrest outside Marquee Restaurant & Lounge.

As you can hear, bystanders and the suspect himself try to lighten the mood -- no pun intended -- as they jokingly offer up their own lighters to the cigar-toting officer.

But, the best quip came from the man filming the whole exchange, who said, "No, don't pull it out. They might think you got a gun!"

St. Louis PD tells TMZ the officer was working secondary employment for Marquee Lounge when they asked him to remove the man from the premises. They also say the man was eventually taken into custody for trespassing on private property and resisting arrest.

In terms of this officer who was seen on top of the guy inhaling tobacco ... SLMPD doesn't have very many answers at the moment as to what led up to this -- but they are officially looking into it at this point.

We're told the department has launched an internal investigation to "better understand the circumstances of the situation, what led up to the video, and the events that transpired after."