Some music critics praised "No Body, No Crime" for its country production and airy quality; others deemed the concept and Haim's contribution underwhelming.

Commercially, the song peaked at number 16 on the Billboard Global 200 chart and reached the top 20 in Australia, Canada, Ireland, and the United Kingdom.

During the COVID-19 lockdowns, Taylor Swift wrote and produced her eighth studio album, Folklore, with Aaron Dessner and Jack Antonoff.

[21] "No Body, No Crime" features twang in Swift's voice[18] and on the guitars[22]—Justin Curto of Vulture opined that her performance is the "twangiest [she] has sounded" since her fourth studio album, Red (2012).

[15] Some publications compared the composition of "No Body, No Crime" to the work of other country musicians, including Martina McBride's "Independence Day" (1994), the Dixie Chicks' "Goodbye Earl" (2000), Carrie Underwood's "Before He Cheats" (2006), and the music of Miranda Lambert.

[52] When "No Body, No Crime" was released, the CEO of the American casual dining restaurant chain Olive Garden, Gene Lee, credited Swift for creating newfound buzz with the brand after she referenced it in the song.

Swift reacted with delight, giving the episode "13 stars" and commenting that she changed Este Haim's name in her phone to "Esther Hollis".

[57] Billboard's Jason Lipshutz similarly viewed it as a delightful song that offers optimism and lightness in contrast to the emotional turmoil of Evermore; he considered it the second best track on the album.

Robert Christgau, in his "Consumer Guide" column, wrote although "No Body, No Crime" was the first track he paid attention to on Evermore, it became his least favorite after repeated listens; he described it as "super-hooky but pat police procedural".

[60] Curto complimented Haim's performance for livening up Evermore's "static pacing", but considered the narrative rather dull and Swift's songwriting not as strong as on her past songs about revenge.

[14] New Statesman's Ellen Peirson-Hagger viewed it as one of the few missteps on the album; he thought the overall sound seemed forced due to the repeated refrain and the lack of vibrant energy that Haim showcase in their music.

[17] "No Body, No Crime" appeared in rankings of Swift's discography by Rolling Stone's Rob Sheffield (181 out of 274)[61] and Vulture's Nate Jones (202 out of 245).