The EAP is designed to help University employees who have persistent personal problems that interfere with their job performance. Supervisors can refer employees who have deteriorating work performance to the EAP for help.
Referral is a way to show concern for the employee as well as for productivity.
You've gotten too involved with the employee's problem and need help extricating yourself. You're planning to meet with your employee and talk about work performance problems, but feel uneasy about how to proceed.