When Does the Film "Batman Returns" (1992) Take Place?
"Batman Returns" is a crime superhero film written by Daniel Waters with Sam Hamm, Wesley Strick, and Tim Burton [adapting the Batman story in "Detective Comics #58 v1 (1941) by Bill Finger, as well as the first Batman story in "Batman" #62 v1 (1950) by Bill Finger and the first Batman story in "Batman" #15 v1 (1942) by Jack Schiff] that released June 19th, 1992. So when is "Batman Returns" set?
It takes place on an alternate timeline of the fictional DC Films Universe in the year:
We know this because at one point Batman/Bruce Wayne says, ..."you're going to think I'm a Norman Bates, Ted Bundy type," refering to the real-world infamous serial killer Ted Bundy was first captured on August 16, 1975 AD. This means it is probably after August of 1975 AD.

1950s? AD
We know this because at one point Batman/Bruce Wayne says, ..."you're going to think I'm a Norman Bates, Ted Bundy type," refering to the real-world infamous serial killer Ted Bundy was first captured on August 16, 1975 AD. This means it is probably after August of 1975 AD.
HOWEVER, clearly, some time (but not a long period of time) has passed since the events of "Batman" (1989), which takes place in 1947 AD. [Though the connections between some Batman movies is contentious among fans, in this story Bruce Wayne/Batman specifically says to Alfred Pennyworth, "Who let Vicky Vale into the Batcave?", referring to an event in "Batman" (1989). It is, in fact, the only time a live-action Batman clearly establishes continuity between stories until "The Dark Knight" (2008), the middle of a trilogy rebooting film series known as The Dark Knight trilogy.]
Additionally, there is a creepy prologue opening the movie that continues under the opening credits of the film and ends with a title card reading: "GOTHAM CITY 33 YEARS LATER". So it must be YEAR AD.
YEAR - 33 = YEAR.
More specifically, both the main action and the prologue take place at Christmastime so we know it is December of YEAR AD and December of YEAR AD, respectively.
It is a chronologically early film in the DC Films timeline (an early film to feature Bruce Wayne/Batman and a first to feature The Penguin and Catwoman) and can be watched at its timeline point.