Under OSHA's recordkeeping requirements, COVID-19 is a recordable illness, and thus employers are responsible for recording cases of COVID-19, if:
The case is a confirmed case of COVID-19, as defined by the Centers for Disease Control and Prevention (CDC);
The case is work-related; and
The case involves one or more of the general recording criteria (medical treatment, days away from work, etc).
OSHA has released revised enforcement guidance that can be reviewed at the following site:
https://www.osha.gov/memos/2020-05-19/revised-enforcement-guidance-recording-cases-coronavirus-disease-2019-covid-19