At-home rapid COVID-19 tests in the U.S. utilize nasal-swab specimens and require high viral loads to reliably give positive results. Longitudinal studies from the onset of infection have found infectious virus can present in oral specimens days before nasal. Detection and initiation of infection-control practices may therefore be delayed when nasal-swab rapid tests are used, resulting in greater transmission to contacts. We assessed whether index cases first identified by rapid nasal-swab COVID-19 tests had more transmission to household contacts than index cases who used other test types (tests with higher analytical sensitivity and/or non-nasal specimen types). In this observational cohort study, 370 individuals from 85 households with a recent COVID-19 case were screened at least daily by RT-qPCR on one or more self-collected upper-respiratory specimen types. A two-level random intercept model was used to assess the association between the infection outcome of household contacts and each covariable (household size, race/ethnicity, age, vaccination status, viral variant, infection-control practices, and whether a rapid nasal-swab test was used to initially identify the household index case). Transmission was quantified by adjusted secondary attack rates (aSAR) and adjusted odds ratios (aOR). An aSAR of 53.6% (95% CI 38.8-68.3%) was observed among households where the index case first tested positive by a rapid nasal-swab COVID-19 test, which was significantly higher than the aSAR for households where the index case utilized another test type (27.2% 95% CI 19.5-35.0%, P = 0.003 pairwise comparisons of predictive margins). We observed an aOR of 4.90 (95% CI 1.65-14.56) for transmission to household contacts when a nasal-swab rapid test was used to identify the index case, compared to other test types. Use of nasal-swab rapid COVID-19 tests for initial detection of infection and initiation of infection control may be less effective at limiting transmission to household contacts than other test types.