When Does "Singin' in the Rain" (1952) Take Place?

"Singin' in the Rain" is a romantic-comedy film written by Betty Comden with Adolph Green and released in a public theater March 27th, 1952. (Wide release was April 11th, 1952.) 

It takes place in the years: 

1927 AD - 1928 AD 

We know this because the first scene depicts the opening night premiere of a fictional silent film titled "The Royal Rascal" and a huge banner at Grauman's Chinese Theatre reads "PREMIERE TONIGHT BIGGEST PICTURE OF 1927" in huge letters. 

Furthermore, one quarter into the movie, the characters react to the "Variety" magazine coverage of the release of the film "The Jazz Singer" (1927) as an "all-time smash in the first week". This tells us it has been a week since the release of that film, which happened in the real world on October 6th, 1927 AD. Immediately afterward, the night of the premiere is referred to as "3 weeks ago" so "The Royal Rascal" premiere is in late September of 1927 AD. 

(Remembered as the first successful 'talkie', i.e. a film with synchronized accompanying sound, "The Jazz Singer" did change things in the real-world Hollywood movie-making industry in the late 1920s.) 

Next, a "Variety" cover displayed on-screen tells us the advent of the 'talkie' has resulted in the statement "Employment figures rose sharply this week over last, declared undoubtedly due to general studio current preparations to change over to sound with a big bang." and the following scenes relatedness to this topic imply this has happened in-between the last scene and the following. So, at least another week has passed, bringing us very roughly to late October of 1927 AD. 

A third through the story, on the night of the first preview of the fictional Monumental Pictures' first sound film, the equally fictional "The Dueling Cavalier", star Don Lockwood says, "Did you ever see anything as idiotic as me on that screen tonight?" then soon holds up a calendar and says, "I feel this is my lucky day, March 23rd" and he's corrected that "It's 1:30 already. It's morning!" This makes the preview night March 23rd and this scene most likely in the early morning of March 24th, 1928 AD. 

The final stretch of the narrative after that scene covers a period of behind-the-scenes remaining film production clearly referred to twice as "6 weeks". This means the film ends in May of 1928 AD. 

3.1928 + 6 weeks (1 month and a half) = 5.1928.