I saw a film during its first indie theater run in the United States in 1998 or 1999; it was in Japanese, and it was about two people (a man and a woman) in their early twenties, one of whom was an emergency responder (perhaps both were?). They stole a bag/parcel of money from a patient that was being transported in an ambulance, and that patient turned out to be a major figure in the criminal world, and they spent the second half of the film trying to outrun his gang.
The film was actually more of a comedy than a drama. I can't think of any more details to better identify it, but I've spent years renting Japanese films and browsing them on Netflix in an attempt to figure out what film this was.
[A subsequent edit] In the middle of the film, they rented a hotel room (I think they spent the day arguing?), and the latter half of the film (closer to the end) featured a low-speed chase, and one of the vehicles was an older-style van (possibly a Volkswagen van similar to the Scooby-Doo Mystery Machine). As in any typical storyline, they broke-up, but then of course, got back together. The argument was possibly over whether or not they should return the money. Sadly, my memory of the film is rather vague, though I do know exactly WHERE I saw it : at a theatre on the southwest arc of Dupont Circle, in northwestern Washington, D.C.
I also recall that they may have driven the ambulance into a lake, in an attempt to conceal some evidence, and they might have tried to drown the patient in it. (Again, this was a comedy. Or at least I found it to be funny, because the violence was sort of slapsticky.)
[Final edit] I think that a lot of my description was inaccurate, due to trying to rebuild the plot from memory. But I definitely recognise some of the scenes from the answer below, which I accepted. Now, off to find it on DVD!