Switch syntax would look something like below:
switch (this.getField("County").value) {
default:
recipient_email = "default@always.com";
break;
case 'county_a':
var am_email = "info@countyA_am.net"
var dsm_email = "info@countyA_dsm.net"
if (am_email == ""){recipient_email = dsm_email}
else{recipient_email = am_email}
break;
case 'county_b':
var am_email = "info@countyB_am.net"
var dsm_email = "info@countyB_dsm.net"
if (am_email == ""){recipient_email = dsm_email}
else{recipient_email = am_email}
break;
}