In what context? The Server application on the device simply requires an Administrator password. And, if you are running from an Administrator account, it won't ask for one.
However, I'm encountering what appears to be a bug trying to user Server.app to connect from my iMac to my (newly installed) Mac Mini... it fails.
However, I can connect from the Mini to the iMac with no problem.
I am having this same issue between my 2012 iMac 27" and my 2007 MBP. I can access/connect to my MBP from my iMac, but when I try to connect to my iMac from the MBP it asks me for my iMac server password. I've been entering my admin password which works on the iMac side to connect to my MBP but it doesn't accept it when entering it in my MBP to connect to my iMac. Have you had any luck with this issue? Is there a separate password for the server? I just received my iMac and the only password I've set up is for my own user/admin account.