"I do not have his book."
Translation:У меня нет его книги.
Yes it is due to the negation.
I found this useful list online. I cannot vouch for its validity though. May be a Russian native can? https://www.cheatography.com/lammmas/cheat-sheets/russian-cases/
It's nominative plural and genitive singular. Here's the full conjugation if you like: https://en.wiktionary.org/wiki/%D0%BA%D0%BD%D0%B8%D0%B3%D0%B0#Declension