The Navy has had 2-crew planes since at least as early as 1944 with the Grumman F7F Tigercat but when did the U.S. Air Force adopt 2-seaters. Does the Navy prefer 2 crew and the Air Force prefers 1? Was the McDonnell F-101 Voodoo one of the first AF 2-crew?
The US Army Air Corps has flown bombers with 4+ crew members since the 1920s, for example the Huff-Daland LB-1 introduced in 1927.
In the WWI and interwar era, a few biplane fighters carried an observer/gunner; the Berliner-Joyce P-16 introduced to the USAAC in 1932 was one such. As aircraft speeds increased through the 1930s, the open-cockpit flexible gun mount became less practical and the weight penalty of a second crew member in an enclosed turret was rejected for fighters.
During WWII the introduction of radars small enough to put on a plane led to the development of "night fighters" or all-weather fighters with a second crew member dedicated to operating the radar equipment. (This Q&A discusses the tradeoffs between single-crew and multicrew designs in more modern combat aircraft.)
The long-range P-82/F-82 Twin Mustang entered USAF service in early 1946. Early models had two identical crew cockpits allowing pilots to alternate control on long flights; later night fighter versions introduced between 1946 and 1948 put the radar operator in the right cockpit.
Depending on what you consider a fighter, the Northrop P-61 Black Widow night fighter entered service with the USAAF in 1944 with a crew of 2 or 3 (pilot, radar operator, and optional gunner).
The Black Widow wasn't a traditional dogfighter, but carried radar and heavy guns to intercept bombers at night.
Similarly, the P-70 was a night fighter in USAAF service from 1942, but it was a conversion of a light bomber design.
I would have to agree that the P61 Black Widow, which carried the formal designation of Pursuit (fighter), was the first multi-crew FIGHTER in the US inventory. It was a dedicated night fighter, and like most multi-crew intercepters, carried additional crew to work the complex weapons systems (or radar, in the case of the P61).
Interesting note: due to special wing flaps, the P61, while not much smaller than a B-25, could roll at about the same rate as a Mustang, though obviously it would lose a lot of airspeed from sharp turns, and take longer to get that speed back.
During the war, a 2 seat night fighter variant of the P38 Lightning, the P38M was produced in small numbers (75 total).
The British did field the Bristol Fighter in WW1, and it was quite successful. They tried this again in WW2 with the Boulton Paul Defiant that was a dismal failure. Plus the German BF 110, which wasn't as bad, but not really competitive with single seaters.