A union spokesman said orchestra players would be casting their votes until 4 p.m. Thursday.
He did not release details.
Management didn't immediately return a call for comment.
Negotiations are continuing with another union, the American Guild of Musical Artists. It represents the chorus, principal singers, stage managers and assistant directors.
The bitter contract dispute has resulted in cancellation of rehearsals for a Feb. 12 opening production of Verdi's "La Traviata" at the Brooklyn Academy of Music.
City Opera moved out of its longtime home at Lincoln Center last year, citing financial troubles. It cut back its usual schedule of 12 to 16 operas per season, with a peak of about 130 performances.
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