Can an employer require a negative COVID test before an employee comes to work? We have discussed it on our [public library system] member directors list but have not come up with a clear yes or no answer.
Here's something positive and affirming I can say: it's possible that the members expressing different opinions on the member directors' list are actually all correct.
That’s because, while I can't give one "clear yes or no answer" to this question, I can give five...five answers based on different scenarios about the facts "before an employee comes to work," including their symptoms, COVID exposure, and the safety measures needed to reduce the risk of COVID transmission in their workplace.
Here the five scenarios are:
Yes, an employer must (and therefore, can) require a COVID test before an employee returns to work, if an employee is symptomatic upon arrival at work or becomes sick with COVID-19 symptoms while at the workplace, absent close or proximate contact with a person with COVID-19.
No, an employer does not have to, and has no basis to, require a negative COVID test before an employee comes to work, if the employee is working 100% remotely at home or in a location not at all controlled or at the direction of the employer.
No, an employer may not require a negative COVID test before an employee comes to work, IF the employee has a medical basis to not be tested; without a negative test, however, if certain screening factors were tripped (such as those in item 2, above) the employer will have to enforce other prescribed measures to comply with state requirements and reduce the risk of transmission within the workplace, such as a mandatory quarantine.
Yes, an employer can require a negative COVID test before an employee comes to work, if an established safety plan based on applicable OHSA guidance and the employee's job duties warrant that level of caution.
I am not surprised you were unable to find a clear answer from a single reliable source, as these five scenario-based answers had to be cobbled together from two separate documents from the New York State Department of Health, which when combined, require employers to:
"Implement mandatory health screening assessment (e.g. questionnaire, temperature check) before employees begin work each day and for essential visitors, asking about (1) COVID-19 symptoms in past 14 days, (2) positive COVID-19 test in past 14 days, and/or (3) close contact with confirmed or suspected COVID-19 case in past 14 days. Assessment responses must be reviewed every day and such review must be documented."
"An individual who screens positive for COVID-19 symptoms must not be allowed to enter the office and must be sent home with instructions to contact their healthcare provider for assessment and testing." [emphasis added]
"If an employee tests positive for COVID-19, regardless of whether the employee is symptomatic or asymptomatic, the employee may return to work upon completing at least 10 days of isolation from the onset of symptoms or 10 days of isolation after the first positive test if they remain asymptomatic."
"If an employee has had close or proximate contact with a person with COVID-19 for a prolonged period of time AND is experiencing COVID-19 related symptoms, the employee may return to work upon completing at least 10 days of isolation from the onset of symptoms."
"If an employee has had close or proximate contact with a person with COVID-19 for a prolonged period of time AND is not experiencing COVID-19 related symptoms, the employee may return to work upon completing 14 days of self-quarantine."
"If an employee is symptomatic upon arrival at work or becomes sick with COVID-19 symptoms while at the workplace, absent close or proximate contact with a person with COVID-19, the employee must be separated and sent home immediately and may return to work upon completing at least 10 days of isolation from the onset of symptoms OR upon receipt of a negative COVID-19 test result." [emphasis added]."
And there you have it. I am not sure if this will make things clearer, but hopefully I have added some clarity to the uncertainty.
 In this case "work" means the "work site," as in an established office or location controlled by the employer where an employee will report to work, or a site they are directed to appear at. For this question, "work site" does not mean a home office or other space the employer does not control/send the employee to.
 I know I covered this in footnote #1, but it bears repeating: based on the published guidance, NY employers are required to conduct mandatory screenings to reduce the transmission of COVID in areas they are responsible for, and areas they serve as part of their work, but not an employee's home office. Requiring a test when there is no logical nexus between the employer's obligations and the request for medical information runs the risk of an ADA violation (not a slam-dunk risk, but enough of a risk to make it a bad idea).
 This answer is based on the Americans with Disabilities Act; if an employee has a disability that means they cannot medically tolerate a test (I have not heard of this, but I imagine it is possible), they will have to provide an alternate means of ensuring safety if such an accommodation is reasonable.
 This answer is based on the needs of work places with the highest levels of risk and risk management.
 "The New York State Department of Health considers a "close contact" to be "someone who was within 6 feet of an infected person for at least 10 minutes starting from 48 hours before illness onset until the time the person was isolated. The local health department should be contacted if the extent of contact between an individual and a person suspected or confirmed to have COVID-19 is unclear. "