If the checkbox gets checked, I would like to put the current address into the permanent address controls

You're going to want to use JavaScript. jQuery is super easy to include in your page and makes the values stoopid-easy to copy.

For example, if you have a button with an ID of make-same, you could do something like this:

$(function(){
    $('#make-same').click(function(){
      // ...do this for each line
      $('#permanent-address-line-1').val($('#current-address-line-1').val());
    });
});

There's actually two parts to this, both using the .val() function.

.val() will return the value of the control if you don't pass any params in, and it will set the value of the control if you do. So here, we're getting the current ($('#current-address-line-1').val()) and using that as the value for the permanent address.

As commented, you'll need to do one per line. There are other tricks with ID filtering, but that's over-complicating the scenario.

EDIT: if you want to clear the boxes on a second click, you can also handle state of the checkbox with jQuery fairly easily.

if($("#isAgeSelected").is(':checked'))
 {
   // copy the addresses
 }
else
 {
   // set the values to blank with .val('')
 }            

Cheers.

Call this function on the Chechbox like:

function checkabove()
{
  if(document.getElementById("chkadd").checked)
  {
    document.getElementById('<%=ddlsecprefix.ClientID %>').value =  document.getElementById('<%=ddlprefix.ClientID%>').value
    document.getElementById('<%=txtsecfirstname.ClientID%>').value=document.getElementById('<%=txtFname.ClientID%>').value;
    document.getElementById('<%=txtseclastname.ClientID%>').value=document.getElementById('<%=txtLname.ClientID%>').value;
    document.getElementById('<%=txtadd1.ClientID%>').value=document.getElementById('<%=txtAddress1.ClientID%>').value;
    document.getElementById('<%=txtadd2.ClientID%>').value=document.getElementById('<%=txtAddress2.ClientID%>').value;
    document.getElementById('<%=txtseccity.ClientID%>').value=document.getElementById('<%=txtCity.ClientID%>').value;
    document.getElementById('<%=txtseczip.ClientID%>').value=document.getElementById('<%=txtZipCode.ClientID%>').value;
    document.getElementById('<%=statesec.StateCombo.ClientID%>').value=document.getElementById('<%=State1.StateCombo.ClientID%>').value;
  }

}