There are a range of answers to this question:
You can print and Save to PDF when managing entries, and then use this PDF in the permitting system.
If you really want the PDF to match an official paper form today, you can use a services like Zapier to connect your forms to WebMerge to generate PDF forms. You can do this today with our JSON post feature and we are about to release an official Zapier app.
We are working on native PDF/DOCX merging as part of Cognito Forms. We are very excited about this feature and know it will be very important to our customers. We expect to have this in place in a few months. You can track our progress on this feature on our Idea Board.
We know full and well that the first option is not sufficient for some organizations, especially government organizations with official forms that must be filled out. Also, the Zapier to WebMerge route is less than ideal (and pricey).
This is why we have always planned to support native merging of form data to PDF and DOCX files. This feature was already on our Next Up list before Adobe announced the "retirement" of FormsCentral, but hearing from their devoted customers has just reinforced the importance of this for us.