Say hi anyway. Be the bigger person.
I agree - there is also no way for you to know why she acts this way. You are all in the same group singing in church, you should be able to be civil and kind to one another. Maybe she thinks - this woman (meaning you) does not seem friendly at all she won't say hi to me. Or maybe it is something else or maybe nothing at all.
Say Hi - pretend you never ever saw a "look". And be overly kind. I tell my kids you don't have to like everyone, but you need to be kind to everyone. Just be kind, polite and friendly.