As tourists flock to Ouray County, including many from states where coronavirus cases continue to climb, officials worry visitors could be carrying and spreading the virus unknowingly, with limited reporting and contact-tracing capability to monitor it.

“We could literally have 100 cases here in Ouray, but they won’t ever count for Ouray because this is not their permanent place of residence,” Ouray County Emergency Manager Glenn Boyd said in an interview last week.

Under direction from the ...