human biology - What is the eye muscle status when you stare at distant view through a glass wall?

In the situation you describe, the eye would be focused on the distant mountain. This would mean that the lens would be stretched and thin in order to minimize the focussing power of the eye. Therefore the ciliary muscles would be relaxed.

When you are looking out of the window, it is possible to make a conscious decision to focus on the window pane itself (thus adjusting the focus to be more powerful as the ciliary muscles contract), however then the distant object will be out of focus and uncomfortable to look at.

This is because the light rays reflecting from the mountain are barely affected by the pane of glass, hence its transparency.