According to the film's official novelisation, the helicopter belonged to the plastics company, Plexicorp. Sulu evidently stole it after tricking the pilot into showing him how it works (since he obviously didn't want the pilot to get freaked out about having to drop the perspex panels off in the middle of the park, to an invisible ship):
Sulu approached the plastics company's big huey, entranced. He had
seen still photos and battered old film of this helicopter, but none
had survived, even in museums, to his time. The huey was as extinct
as the humpback whale. He stroked one hand along its flank.
"Oh, I think so, eventually," Sulu said, trying not to sound too certain. He drew the conversation back to the huey. "I was hoping I'd find a pilot when I saw this helicopter. Mind if I ask a few questions?"
They chatted about the copter for a while. The pilot glanced at his watch. "I've got to make a delivery," he said. "Want to come along?"
"I'd like nothing better."
In the next scene, there's no pilot evident and Sulu is at the controls.
There was a similar scene in the film's original script (most of which made it into the film). Again, the implication is theft rather than hiring:
112 EXT. PLEXIGLASS FACTORY - BIG YARD - DAY
Sulu moves through the grounds where Plexiglass Products of all shapes
and sizes are stacked. In the midst of this, sits a great HUEY
helicopter with the company logo on its side. Its PILOT is working on
his engine as Sulu comes up touches the craft lovingly, stares
studiously into the cockpit.
SULU: Hi. Huey 205, isn't it?
PILOT: Right on. You fly?
SULU: Oh, here and there. (pats it) I flew something similar in my Academy days.
PILOT: All right, then this is old stuff to you.
SULU: Old, yes. But interesting. (then) Do you mind if I ask a few questions...?
Note the sheets of perspex in the background.