Background: To assess and limit the SARS-CoV-2 exposure risk from symptomless individuals in the hospital setting, molecular and serological screening of staff and patients attending a tertiary hospital in China was conducted. Methods: SARS-CoV-2 RNA was tested by quantitative RT-PCR. Anti-SARS-CoV-2 IgM and IgG were screened initially with two lateral flow immunoassays (LFIs) and further confirmed with three chemiluminescence immunoassays (CLIAs). The assay performance was assessed using archived samples from 32 confirmed COVID-19 cases and 80 healthy individuals. Results: Between April 24 and May 8, 2020, 16,043 subjects (7,392 medical staff, 4,714 inpatients, 1,209 chaperones, 1,705 outpatients, and 1,023 fever clinic patients) were screened. No subject tested positive for viral RNA. Seventy-three (0.46%) tested positive for IgM or IgG on the initial LFI screening, of whom 63 were investigated with CLIAs: 2 (0.01%) were confirmed as seroreactive and 18 (0.11%) were indeterminate. Unconfirmed seroreactivity was significantly more frequent in fever clinic patients. The CLIAs showed similar (95.0-100%) IgM or IgG specificity but higher IgG sensitivity (93.75-96.88% vs. 31.25-81.25%) than the LFIs. The confirmed seropositive cases included a previously discharged COVID-19 patient and an undiagnosed symptomless patient showing detectable IgM and IgG over 35 days of follow-up. No transmission was evidenced within the corresponding family cluster. Conclusions: Low SARS-CoV-2 prevalence and limited exposure risk were observed. Seroprevalence varied between 0.012% and 0.12% according to the testing algorithm and the confirmation criteria used, indicating that quality standards for serological tests are needed. Protective immunity in asymptomatic COVID-19 patients who recovered needs to be investigated further, but the associated risk of transmission appeared limited.