Identification of societal activities associated with SARS-CoV-2 infection may provide an evidence base for implementing preventive measures. Here, we investigated potential determinants for infection in Denmark in a situation where society was only partially open. We conducted a national matched case-control study. Cases were recent RT-PCR test-positives, while controls, individually matched on age, sex and residence, had not previously tested positive for SARS-CoV-2. Questions concerned person contact and community exposures. Telephone interviews were performed over a 7-day period in December 2020. We included 300 cases and 317 controls and determined odds ratios (ORs) and 95% confidence intervals (95% CI) by conditional logistical regression with adjustment for household size and country of origin. Contact (OR 4.9, 95% CI 2.4-10) and close contact (OR 13, 95% CI 6.7-25) with a person with a known SARS-CoV-2 infection were main determinants. Contact most often took place in the household or work place. Community determinants included events with singing (OR 2.1, 95% CI 1.1-4.1), attending fitness centres (OR 1.8, 95% CI 1.1-2.8) and consumption of alcohol in a bar (OR 10, 95% CI 1.5-65). Other community exposures appeared not to be associated with infection, these included shopping at supermarkets, travel by public transport, dining at restaurants and private social events with few participants. Overall, the restrictions in place at the time of the study appeared to be sufficient to reduce transmission of disease in the public space, which instead largely took place following direct exposures to people with known SARS-CoV-2 infections.