When Does "Rush Hour" (1998) Take Place?
"Rush Hour" is a comedy crime film written by Jim Kouf with Ross LaManna that released September 18th, 1998. So when is "Rush Hour" set?
It takes place in the year:
We know this because the July 1997 AD prologue is followed quickly by a time and place setting title card that reads "AMERICA Two months later". So the story's main action seems to start in early September of 1997 AD.

1997 AD
We know this because the July 1997 AD prologue is followed quickly by a time and place setting title card that reads "AMERICA Two months later". So the story's main action seems to start in early September of 1997 AD.
7.1997 + 2 months = 9.1997.
The narrative ends just a matter of days (or, at most, a full week) later, within the 1997 AD calendar year.
Additionally, there is a prologue that halfway through includes its own time and place setting title card: "HONG KONG Last day of British rule" and the following scene corroborates this. This happened in the real world and the famous hand-over took effect at midnight on July 1st, 1997.