When Does "The Naked Gun" (1988) Take Place?
"The Naked Gun: From the Files of Police Squad!" is a comedy crime film written by Jerry Zucker with Jim Abrahams, David Zucker, and Pat Proft that released December 2nd, 1988. So when is "The Naked Gun" set?
It takes place in the year:
We know this because the real-world Iranian supreme leader Ruhollah Khomeini (1900-1989) appears in the opening sequence. He died on June 3rd, 1989 AD in the real world so it is most likely before June of 1989 AD.

1986 AD or 1987 AD
We know this because the real-world Iranian supreme leader Ruhollah Khomeini (1900-1989) appears in the opening sequence. He died on June 3rd, 1989 AD in the real world so it is most likely before June of 1989 AD.
Later, about halfway through the movie Lieutenant Franklin 'Frank' Drebin and Jane Spencer go on a date and they step out of a theater where the marquee displays "PLATOON" laughing hysterically. The film "Platoon" (1986) debuted in theaters on December 19th, 1986 AD. So it must be after late 1986 AD.
More specifically, the real-world baseball player Reggie Jackson appears during his professional baseball career and he retired from professional baseball on October 4th, 1987 AD. So it must be before late 1987 AD.
Therefore, it takes place between early December of 1986 AD and early October of 1987 AD. Probably in 1987 AD but possibly in very late 1986 AD.
It is the first film in the Police Squad! universe and can be watched at its timeline point after the TV series "Police Squad!" (1982) and before "The Naked Gun 2½: The Smell of Fear" (1991).
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