Ancestry.com in libraries is called Ancestry.com Library Edition. It is a great resource, but the content differs from the subscription database. Here is a 2013 guide to the differences. (This will open as a .pdf, in a separate window.)
This guide is put out by ProQuest, the company that sells AncestryLibrary Edition. It refers to other ProQuest databases for places you can find the information. One database it refers to is Heritage Quest, which is available to all Michigan libraries through MEL.
It is worth noting that PERSI is also available from FindMyPast.com. This is a subscription site, but you can search PERSI for free in it. (You may have register, for free, before it will let you search.)