To study the spatial disparity of the COVID-19 infection in counties of Minnesota, we developed Bayesian conditional autoregressive models, non-adaptive or locally adaptive models, for both 1-year case data and the cases during the winter outbreak 2020. Our models consistently led to high posterior estimates of spatial dependence parameter(s), indicating spatially structured relative risks (RRs) over the counties. Clusters of high RRs in Southwestern counties were observed for both the 1-year and the outbreak data. Northeastern counties showed low RRs for 1-year infection. County-level characteristics, such as demographics, housing, employment, and education partially explained the infection risks and the local dependency exhibited in 1-year data, as well as reduced the variation of the random effects. For infection during the outbreak, however, none of the covariates analyzed was significant. This may indicate that the spatial variation of RRs during the outbreak, captured by our models, was due mainly to the transmission nature of this infectious disease.