Is there a locally hosted version of jotform?

By saying locally hosted, do you mean to say a licensed software of running JotForm? If so, unfortunately, we do not provide such. If you wish to run a JotForm builder on your website, I would suggest using JotForm Anywhere (https://www.jotform.com/anywhere/). 

But if I am misunderstanding your inquiry, please let us know.

Thanks.