Firstly, “Take Out Some Insurance On Me, Baby” was a single release for Tony Sheridan and The Beat Brothers in 1961. Of course, The Beat Brothers was a pseudonym for The Beatles. Recorded in 1961, the recording resurfaced after The Beatles became famous. Then, in 1964, it became available on singles** and an album.
** B-side to “Ain’t She Sweet” (Germany and UK), also B-side to “Sweet Georgia Brown” (US).
In Detail
Album/Single
Recorded: 24th June, 1961
Studio/Location: Studio Rahlstedt, Hamburg, Germany
Format: 7-inch single (B-Side) (A-side being “Ain’t She Sweet” (UK))
Genre: Rock, blues
Track Duration: 2:52
Record Label: Polydor Records NH 52-317 (UK)
Songwriters: Charles Singleton, Waldenese Hall
Producer: Bert Kaempfert
Engineer: Karl Hinze
Performers**
Tony Sheridan: vocals
John Lennon: rhythm guitar
Paul McCartney: bass guitar
George Harrison: lead guitar
Pete Best: drums
** Ringo Starr was not part of the Beatles in 1961, of course.
Track Sources

Take Out Some Insurance on Me, Baby (Single) (1964)

The Beatles’ First Album (1964) (Germany)
7″ Single
The Beatles’ First (Germany)
Take Out Some Insurance On Me, Baby
The song was a single*** for Jimmy Reed in 1959 in the US, but it never made the American charts. However, while in Hamburg, Germany in 1961 The Beatles were covering old songs such as this. Of course, in those days The Beatles were just scraping out a living and didn’t have their trademark name yet.
*** For this single, credits went to Jesse Stone, but on The Beatles’ UK single, credits went to Charles Singleton and Waldenese Hall.
The song title also has many variants too. For example, “If You Love Me, Baby (Take Out Some Insurance on Me, Baby)” and “Take Out Some Insurance on Me, Baby (If You Love Me, Baby)”.
Recording Studio
In short, the band began recording “Take Out Some Insurance On Me, Baby” on the 24th June, 1961 at the Studio Rahlstedt, Hamburg, Germany. This was also the last of three days recording with producer, Bert Kaempfert.
In Germany, the song was on “The Beatles’ First” album which also had other recordings from their Hamburg days. However, after The Beatles became famous, it came out on a single in the UK with the A-side being, “Ain’t She Sweet”. The release date in the UK was 29th May, 1964, and it got to number 29 in the charts.
In America, the authorities thought the line towards the end of the song, “Oooh some goddamn insurance on me baby” was inappropriate for radio. So, the Atco label which released it, edited that language out.