Suppose you have an employee with fever during the covid-19 pandemic. Is there any law which makes mandatory to report your employee to the doctor, health authorities, or whatever for him/her to make a covid-19 test to check if he has the disease or not, or are the employers completely exempt of this duty?
There is no Federal or State law currently that has this type of requirement.
A lot of employers, especially larger ones, have health screening and may reject an employee access to the property until they are tested, but this is voluntary by the employer (not the employee). For example, my employer asks that we complete an online questionnaire before going to work, and will take our temperature at the door. Anybody who fails the questionnaire or the temperature test is asked to return home until they can pass it. Notice that it doesn't say anything about requiring COVID testing, just that they need to remain home until they've been symptom free for 24 hours.
Some other facilities, especially long-term or senior care are mandating that employees are tested, some as much as twice weekly. These testing guidelines are in place mostly by the recommendation of the CDC but there is no law mandating it as of today.