AWS Route 53 CNAME - dot at end of target value or not?

My hosted zone at AWS seem to be working fine so I am a little nervous about changing it -- but I noticed that my CNAME record for my white-label DNS looks like this right now (no trailing dot):

*.localroute.net.    CNAME    localroute.net    -    -    172800

Is this working correctly because the system is smart enough not to append another "localroute.net" to the value? Or should I just go ahead and add the dot at the end so it looks like this:

*.localroute.net.    CNAME    localroute.net.    -    -    172800

Also, am I correct in saying that if I want one domain to map to another via CNAME then the format must have the dot at the end, to avoid ambiguity? E.g.:

www.example.net.    CNAME    example.com.    -    -    172800

Thanks for any insight you could give me on this, I want my DNS to be perfect :-)

From the Route 53 documentation on record values:

CNAME — Canonical name
The fully qualified domain name (for example, www.example.com) that you want Amazon Route 53 to return in response to DNS queries for this resource record set. A trailing dot is optional; Amazon Route 53 assumes that the domain name is fully qualified. This means that Amazon Route 53 treats www.example.com (without a trailing dot) and www.example.com. (with a trailing dot) as identical.

However, even if you had been dealing with an administration interface that is not as clearly documented, you could just try it and see how the values are used before doing your actual changes (obviously doing the testing well separated from anything used for production).