The number of cases was sharply up from the nine reported on the opening day last year, but police put it down to the greater readiness of victims to report crime.
The complaints ranged from harassment to one reported rape, police said, adding that on average, around 50 sexual offences are recorded annually during the week-long carnival.
Police in the western German city have been struggling to restore public confidence after hundreds of women said they were groped and robbed in a mob of mostly North African and Arab men during New Year festivities.