In both the OG RE2 and the remake, the T-Virus is released into Racoon City when rats consume the formula after vials containing it are destroyed. The vials are destroyed during a fight between a mutated William Birkin and Hunk's squad.

However, it is unclear to me whether Birkin intentionally released the T-Virus and (Infected) Racoon City or not. The most believable reason to do this being to 'Get Revenge against Umbrella'

In the OG cutscene, Birkin can be seen perhaps intentionally, Crushing certain vials. Whether this was meant to imply Birkin's intentions or not, is unclear. It is possible he simply stepped on a vial unintentionally while in his monster form.

In the remake cutscene however, it is very clear that Birkin accidentally destroys the vials containing the virus.

OG - https://youtu.be/alStb3nw0Xs?t=103

RE - https://youtu.be/WJ0uOh9UcFM?t=331

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The question being... was Birkin originally meant to have been portrayed as 'willingly' infecting Racoon City. Or was it always just a by-product of his rampage