Not sure that I would agree with using a checkbox for this situation. An HTML checkbox field allows the user to make 0 or more selections. If you do want to use a checkbox, you need to decide a true/false value for when it is checked and a true/false value when it's not checked. In your code to parse the HTML form input from the user, the checkbox's name will only show up in the paramater list if it was checked. So you'll need code to first determine if it is in the parameter list.
Personally, I would recommend going with radio buttons instead. HTML radio buttons allow the user to select only 1 value and does allow you to preset a default value. In this case, your values would be true and false. Also, your radio button value will always be in the parameter list.
Also, I should mention that this sounds more like an HTML design question rather than a Perl question. Are you having problems with Perl code to create the HTML form? Or Perl code to deal with user input from the HTML form? Or both? Or something else?