Theories of agency--the feeling of being in control of one's actions and their effects--emphasize either perceptual or cognitive aspects. This study addresses both aspects simultaneously in a finger-tapping paradigm. The tasks required participants to detect when synchronization of their taps with computer-controlled tones changed to self-controlled production of tones, or the reverse. For comparison, the tone sequences recorded in these active tapping conditions were also presented in passive listening conditions, in which participants had to detect the transition from computer to human control, or vice versa. Signal detection theory was applied to separate sensitivity from bias. Sensorimotor cues to agency were found to increase sensitivity in the active conditions compared with the passive conditions, which provided only perceptual cues. Analysis of bias revealed a tendency to attribute action effects to self-control. Thus, judgments of agency rely on veridical sensorimotor cues but can also be subject to cognitive bias.