I gave the script as per details you mentioned in earlier notes

In that case, you have to restrict the group membership based on assigned to users via reference qualifier. Please refer below link for more info.

4.3.2.2 section here

http://wiki.servicenow.com/index.php?title=Reference_Qualifiers#gsc.tab=0

P.S: In that case your updated script is

current.assigned_to = gs.getUserID();

if(gs.getUser().isMemberOf(current.assignment_group)){

}

else {

current.assignment_group = "";

}

current.update();