Your first parameter will be used as the filter and passed along as 'term'. You can additionally pass other parameters via the URL, assuming they are accessible dynamically like so:
$('#txt_name').autocomplete({
source:path+'get_person.php?city='+$("#city").val()+"&name="+$("#name").val(),
select:function(event, ui){
alert(ui.item.name);
}
});
Where your form contains two input elements ID'd as 'name' and 'city'.
Then, in your script that performs the query, you'd have access to the filter with $_GET['term'], and access to your city and name variables with $_GET['city'] and $_GET['name'], respectively.
Of course, it looks like you will be searching for a person and filtering by their name? In that case, you don't even have to pass along &name=... as term will contain the filter data you are looking for.