Female canaries can sing, but they don't do so as frequently, as fluently or for as long of a time as male canaries. This is because male canaries' singing behaviors are driven by their hormones, especially testosterone.
Male canaries sing their familiar long, flowing songs to attract mates, to signal where their territory boundaries lie and to indicate their health and strength to all potential challengers. Female canaries, however, can make a series of trills, warbles and other sounds that might be mistaken for a male's song by someone who is not knowledgeable. Females especially like to do this if a male is available to imitate.