On 23 July 1975, the new constitution of the State of Rio de Janeiro established that the flag and the shield of the new state (which was absorbing Guanabara) would be the same that those of the ancient state. The blue and white are the traditional colors of Portugal.
According to articles 8 and 10 through 12 of law no. 5588 of 5 October 1965, the flag is 7:10, divided quarterly white and blue-celeste, with the white in the upper hoist and lower fly, with the state coat of arms on the center.
The current flag law is from 1965 and makes no mention of any earlier state flag. However, Whitney Smith says the flag was adopted in 1947. I have thus far been unable to verify the 1947 adoption date from laws and decrees published in the state's Diário Oficial for 1947.
A set of cards distributed with bars of Eucalol soap in the 1930s shows Rio de Janeiro state with the same flag as that used today except that the style of the coat of arms is consistent with its appearance in the 1920s and 1930s. Obviously this flag dates from before the reported adoption date of 1947, at least de facto. It is possible that 1947 was when it was readopted following the 1937-46 period in which state flags were legally banned.
I know the current flags and coat of arms are from an official source (state government site), but there is one small error. It's very common in Brazil that the governments themselves publish their symbols with heraldic errors. Where it's described as "silver" in the badge, for some odd reason they painted it grey! This doesn't exist in heraldry. "Silver" means the metal itself, when the badge is on a plate, or white when on flags, papers etc... Never grey!