I just remember the last section bit where Conan & Sonoko(?) forced to make emergency landing on some harbor(?). I think the real Pilot & Co-Pilot got poisoned by accident because they are kissing the victim hand without their gloves.
This is not an OVA, but rather a movie. The title is:
It is the 8th movie and one that features Kaitou Kid. The last part goes like this:
While flying the plane, it's struck by lightning. They activate the back up generator. They see that the auto-pilot is broken down so they have to cancel the landing. They manage to pull up but lose one engine in the process and damage the runway. The next thing they notice is that there isn't much fuel left. This is because when everyone was in the cockpit, Ban accidentally hit the fuel gauge button which made the fuel (in separate engines) go into one big tank.
Conan finds a place to land (Sakamori Dock). Kid (in disguise of Shinjo) says he can't do it because he injured his hand and that Ran should take his place. Kid opens the emergency hatch and tells them good luck. Kaitou Kid then jumps from the plane. Nakamori chasing the real Shinjo, notice the real kid flying, and so they chase after him.
Conan tells Sonoko to take his place and that he has to go to the washroom, also to put on the headsets in case contact is made with the airport again. Conan uses his voice-changing bow tie and tells Ran using Shinichi's voice. Ran tells him to stop acting so cool and that the fate of these passengers is within her hands. She then tells him that she loves him which makes him go silent. She tells him that she see's a ribbon of red lights. Heading towards the dock. Conan sees it and realizes why Kid jumped off. He was going to attract the lights of the police to create a runway so they can see.
Ran successfully lands the plane. Ran thinks that the person who jumped was Kaitou Kid's accomplice and she was talking to Kaitou Kid. She is relieved to know her secret wasn't let out.
Last part summary quoted from the page itself