Individuals with congenital amusia usually exhibit impairments in melodic contour processing when asked to compare pairs of melodies that may or may not be identical to one another. However, it is unclear whether the impairment observed in contour processing is caused by an impairment of pitch discrimination, or is a consequence of poor pitch memory. To help resolve this ambiguity, we designed a novel Self-paced Audio-visual Contour Task (SACT) that evaluates sensitivity to contour while placing minimal burden on memory. In this task, participants control the pace of an auditory contour that is simultaneously accompanied by a visual contour, and they are asked to judge whether the two contours are congruent or incongruent. In Experiment 1, melodic contours varying in pitch were presented with a series of dots that varied in spatial height. Amusics exhibited reduced sensitivity to audio-visual congruency in comparison to control participants. To exclude the possibility that the impairment arises from a general deficit in cross-modal mapping, Experiment 2 examined sensitivity to cross-modal mapping for two other auditory dimensions: timbral brightness and loudness. Amusics and controls were significantly more sensitive to large than small contour changes, and to changes in loudness than changes in timbre. However, there were no group differences in cross-modal mapping, suggesting that individuals with congenital amusia can comprehend spatial representations of acoustic information. Taken together, the findings indicate that pitch contour processing in congenital amusia remains impaired even when pitch memory is relatively unburdened.