Does the addition of water to N2H4 produce N2H4 I am currently calculating the $\ce{pH}$ of a species. 

The reaction is as follows, 

$$\ce{N2H4 + H2O &lt;=&gt; N2H_{$A$}+ + OH-}$$

However, I'm not sure what the value of $A$ will be. In my textbook it says $4$, which is stumping me as in every other example with a weak base the subscript increases. 

What is the value of $A$ and why?
Yes, equations must be balanced, thus the only correct way to write this is:

$$\ce{N2H4 + H2O &lt;=&gt; N2H5+ + OH-}$$

Easy to remember: Nitrogen typically has a free electron pair which can act as a Lewis base for a proton.

If your textbook says $4$, it is an error in your book. Good job on spotting it and realising it.