posting the client certificate along with the form data to the server

How can we achieve the folowing:

When one of our browsing clients uses their browser to fills out one of the web site forms, how do we:

post the client certificate along with the form data to the server?

Or sign the form data with the client certificate before posting to the server?

Each browsing client (using the browser to display the web site) has their own private certificate on their local machine. Our clients are our collaborators

Thank you :)