Hey E.,
I would tell her truth... but on her level.
People die, and it can be scary. People die because their bodies get too old or sick, and they stop working. They turn off. If it were me I would explain that people die just like other things you see die, like plants, flowers, animals... their bodies get tired or sick and their light goes out. Use terms that she will be familiar with. Saying someone's "light goes out" sound weird to us but to a 3 year old, the concept is easier to grasp because she knows that it looks like when a light is on and then turns off.... or another example you can come up with that you know she'll be better able to grasp.
I taught preschool for quite a while and I had a few situations like this one when a child would lose a relative and would ask questions and what not for a few weeks.
There are books out there about it too, some really great ones. Check the kid's section at a bookstore in your area, there should be lots.
The best thing to do is be honest, because in the end thats all you can be. She will react to your reactions... so if you approach it as scary and creepy and "doom"-ish... yeah, it'll freak her out. But be level headed and explain that its just something that happens, and reassure her in whatever ways you can.
We are personally a spiritual family but even then - I wouldn't teach my kids about the concept of heaven. Its a lot to grasp, and teaching them about some far away place where nobody is hurt and God lives will immediately translate into a fairytale for her, and then eventually unbelief as an adolescent and adult. I was an atheist for years because I was raised to think that people floated off to mansions in the sky when they died - and when I hit 13,14,15... I thought, "Well thats stupid." And all of my upbringing went out the window. (Sorry, but it did.)
I'm sorry for your loss, best of luck to you!