Which users have permission to use Petty Cash?

You can either permit access to all Petty Cash accounts within 'User Settings' > 'Manage User roles'. You can either give 'view only' permission or standard permission.

Or you can give access to a specific Petty Cash account within the Bank & Petty Cash Account Settings:

To help you better understand the Petty Cash module as a whole, please visit the module overview page here.