Though languages are often associated with one primary writing system, often another can be adapted for use.
Look at how Vietnamese was classically written with a form of Chinese characters, but in modern times is written in Latin script using a system adapted from Portuguese.
I think your question is still a good one (which I don't know the answer to) but it's worth being precise with the terminology :)
The writing system that developed with Sanskrit and that's still used for both Sanskrit and several modern languages of India is called Devanagari.