During a discussion with my boss about multiple projects and deadlines, she said that I looked stressed and should use the company EAP program to get therapy. Can she say that? It wasn't in an informal setting. It was a closed door, in her office meeting with me.

Sure they can... why would they not? They saw a problem, suggested something the company would pay for to resolve the problem to keep you around... they could have simply fired you over an attitude issue or stress they perceive.

And really... many places would rather do just that. They really don't even need a reason. Consider it a compliment they value you being there.

And thank her for saying that to you behind closed doors and not in the staff lounge in front of your colleagues. Yes, I agree she cares about you and wants you to stick around.

Now, what about therapy? Even just a few counseling sessions to relieve that stress?

I doubt she used the words 'mental therapy.' Therapy is often just counseling in ways to relieve stress and to deal with many problems throughout the day, and doesn't imply that someone has a psychiatric diagnosis.

Most likely while they can't force you into EAP, often if you don't, your job is at risk. While in the EAP program, at times you have some protection from job related issues due to that.

The are actually required to offer it to you, esp if the see future disipline issues coming from this. Your boss has now cleared the issue if you refuse this and they have to write you up or fire you. They offered the help.

This offer will most likely be documented in writing and a record keep of it