Типа такого...
var obj = {val: "aaa"};
var test =
{
o1: obj,
o2: obj
};
alert(test.o1==test.o2);
localStorage.test = JSON.stringify(test);
localStorage.test1 = JSON.stringify(obj);
test = JSON.parse(localStorage.test);
obj = JSON.parse(localStorage.test1);
test.o1=obj;
test.o2=obj;
alert(test.o1==test.o2);