Is artificial grass approved by local authorities?

I see a lot of artificial grasses installed even in public areas so I'm just wondering.

Well the answer to your question can be different from region to region. As far as I know that there is no local authorities have regulations to either approve or restrict the artificial grass applications. However, some homeowner associations might have their own rules or regulations for their own communities, in such case, you will need to find out the specifics from your HOA. We offer free consultations, if you can fill out this online form, we can help you to dig out more details regarding your question:
https://megagrass.com/pages/free-estimates

If it was installed in a public place, then yes I guess it is approved.

I don't see any reason why it won't be approved. Most officials even promote the use of artificial grass.