The voiceover about McConaughey's potential double oscar/emmy win last night made me think of this.
Michael Moriarty won a lead Tony and a supporting Emmy in 1974. No other best lead actor in a play won an Emmy in the same season. But maybe one of the musical Tony best actors won a lead Emmy that year.
Christopher Plummer won the Best Leading Actor Tony for "Barrymore" and Outstanding Leading Actor in a Limited Series Emmy for "The MoneyChangers" in 1977
Ellen Burstyn won the Tony Award for Same Time Next Year in 1975 and the Oscar for Alice Doesn't Live Here Anymore at the 1975 awards (the film was released in late 1974). That's not Tony and Emmy, but still noteworthy.
Off topic (Oscar rather than Emmy), but as with Ellen Burstyn above:
Shirley Booth won the lead Tony in 1953 for TIME OF THE CUCKOO, and won the 1953 lead Oscar for the 1952 release COME BACK, LITTLE SHEBA (for which she'd won the lead Tony in 1950).
Audrey Hepburn won the lead Tony in 1954 for ONDINE, and won the 1954 lead Oscar for the 1953 release ROMAN HOLIDAY.
Mary Martin won both the 1955 Tony Award for Lead Actress in a musical (PETER PAN) and the 1955 Emmy Award for "Best Single Performance" (for the first PETER PAN live broadcast).
But of course, henrik's question regards actors... and remains unanswered.