What is another word for when a mechanical door-lock clicks in?

I'm talking about those doors that have mechanical locks that 'click' automatically when the door is closed and need a handle/knob to be moved to open them again. I'm using this in a sentence:

He walked towards the door to check in case it hadn't clicked in.

I made 'clicked in' up. I'm not sure if there is a better word/phrase out there to replace 'clicked in'.

I would say that the door is "latched" if it can be opened from either side, "locked" if it can only be opened from one side without a key or code (fire codes usually specify that one must be able to exit a room unimpeded).