Is a person who doesn't spend money, petty?

Not necessarily.

how about a person who is wealthy, but refuses to spend it?

miser?

http://www.merriam-webster.com/dictionary/petty

http://www.merriam-webster.com/dictionary/miser?show=0&t=1317595026

I have to relate spending money to pettiness

do you think a person who is wealthy, but refusese to spend it for others, an okay example of spending money to pettiness?

Thank you in advance :)

A petty rich person may spend his money on unimportant things or cut a child out of her will for little reason.

would not spending his money at all, still be petty behavior

because it is "marked by narrowness of mind, ideas, or views, lack of generosity"

Determining whether someone is petty based solely on their spending habits can be subjective and dependent on the context. Not spending money could be a result of personal financial constraints, frugality, or simply choosing to prioritize saving over expenditure. It is crucial to avoid making broad assumptions or judgments about individuals based solely on their spending habits. Instead, it's advisable to consider the reasons behind their financial choices and have an open-minded perspective. If you are curious about someone's motivations or behaviors regarding money, having a respectful conversation with them can provide more insight into their perspective.