{"Status":"OK!","ListaPermessi":
[{"IdPermesso":10,"Nome":"WIND_PARAMS"},
 {"IdPermesso":11,"Nome":"ADMIN_SERVER"},
 {"IdPermesso":21,"Nome":"REC"},
 {"IdPermesso":22,"Nome":"REC_DIST"},
 {"IdPermesso":23,"Nome":"REC_DIST_CR"}
]}

var parsedResult = JSON.parse(result); // where result is the above JSON
if (parsedResult.Status === "OK!") {
    // Set sessionStorage vars
    if (typeof(Storage) !== "undefined") {
        // localStorage & sessionStorage support!

        sessionStorage.setItem("ListaPermessi", parsedResult.ListaPermessi);
    }
    else {
        // Sorry! No web storage support :(
    }
}

sessionStorage.setItem("ListaPermessi", JSON.stringify(parsedResult.ListaPermessi));

if (typeof Storage !== "undefined") { //...