You have to fetch field value using .value
as you are passing whole object to the URL as document.getElementbyId('value')
returns whole field object.
var dist = document.getElementById('value').value;
So your function should be like this
function check() {
var dist = document.getElementById('value').value; // change here
if (dist != "") {
window.location.href = "district.php?dist=" + dist;
} else
alert('Oops.!!');
}