Unfortunately this widget works in a side bar and appears on every page. If you want to use it on a static page then you need to copy the code to your static page and edit the template to stop it appearing in the side bar.
I found the instructions here:
http://helplogger.blogspot.co.uk/2013/05/new-blogger-widget-contact-form-change.html
It was easy to do and works well, but remember not to delete the widget otherwise it will stop working entirely. It will also only send to the email address your blogger account is registered to (usually a Gmail or Google Apps account).
This is what it looks like on the page:
