You can rip DVD's from the library at home and the library won't know about it.
If you do however borrow a lot of DVD's at the same time such as checking out 300 or more they may suspect that you're copying or ripping the DVD's.
You can't rip the DVDs from the library using the library computers but you can do so at home.
I've borrowed DVDs from my library and have ripped them and nothing has happened to me and the library didn't know.
Ripping DVDs for personal use is technically illegal but not often enforced.
However it is also illegal to circumvent the copy protection mechanisms on DVDs.
It's also illegal to Rip DVDs with the intent to sell them.
The DMC or Digital Millennium Copyright Act criminalizes the use of any tools which circumvent digital rights management software on DVDs.
Although the DMCA does allow for some exceptions like for students and professional educators.