Integration of information across different senses is a common property of cortical neurons. Somatosensory input impacts on auditory cortical processing through a mechanism that suppresses sound-evoked activity (Lohse et al., 2021). We carried out a number of experiments to investigate a) the perceptual implications of this crossmodal integrative process and b) its context dependence. In order to assess whether somatosensory suppression of sound-evoked activity affected the ability of mice to detect acoustic stimuli, we first performed a near-threshold sound detection experiment. While simultaneous whisker stimulation suppressed sound-evoked activity in the auditory cortex, measured using two-photon calcium imaging, and decreased detection latencies, it had no effect on detection thresholds. Second, we trained mice in a go/no-go task to discriminate tones of different frequencies, which revealed that discrimination thresholds were lower for tones presented together with stimulation of the whiskers compared to tones presented on their own. Finally, we carried out an experiment in which we either rewarded mice to detect sounds or to detect stimulation of their whiskers. Somatosensory suppression of sound-evoked activity was stronger when mice were engaged in the whisker detection task and weaker when they were engaged in the sound detection task. We conclude that somatosensory-auditory suppression in the auditory cortex depends on behavioural context and improves auditory discriminability while leaving detection thresholds unchanged.