Kitty, I was not a supervisor, but I did work in human resources for 15 years for a public agency and had worked with many supervisors and legal counsel regarding employee disciplinary matters. As her supervisor, you should maintain a professional demeanor and avoid a personal relationship with subordinates. I have witnessed many good intentioned supervisors have the subordinate turn the situation around on the very person trying to be a friend and offer support. This can often lead to litigation.
I would recommend that you discuss this matter with HR (not disclosing your suspicions of alcoholism) and have them guide you through a written “special evaluation” where your concerns regarding performance and/or excessive absences are discussed with the employee. Refrain from discussing “personal” problems should the employee divulge, as this could be used against you in the future as “discrimination” should a disciplinary action ensue. Direct the employee to discuss with HR the available programs through the state; many public agencies contract with a mental healthcare program for free counseling outside of their medical insurance (MHN). This offers additional confidentiality for the employee. The employee does not need to inform HR of their personal problem. He/she can simply state that they are having personal issues and would like information on counseling services.
A specific time period, i.e., 3 – 6 months, should be set for a follow-up evaluation.
I know you want to help, but as I wrote earlier, you have to be very careful to not put yourself in a bad situation that could jeopardize your position and personal recovery.
State and public employers are easy targets for attorneys soliciting new clients for workplace discrimination claims. While the majority are nuisance claims that eventually settle outside of court to avoid the high litigation costs, some are legitimate. Best of luck.