Adding Google Custom Search to a Public Released Theme

You can improve it, combining Google Search and WordPress Search. using this simple javascript:

function displaygoogle(checkbox){
    if(checkbox.checked){
        document.getElementById("googlesearchbox").style.display = 'block';
        document.getElementById("wordpresssearchbox").style.display = 'none';
        document.getElementById("googlesearchinput").value = document.getElementById("wordpresssearchinput").value;
    }
    else{
        document.getElementById("googlesearchbox").style.display = 'none';
        document.getElementById("wordpresssearchbox").style.display = 'block';
        document.getElementById("wordpresssearchinput").value = document.getElementById("googlesearchinput").value;
    }

}

see more detail here: http://jaider.net/2011-05-08/how-to-combine-google-wordpress-search/