Here's the RCA specs on the set:
http://tv.rca.com/en-us/modeldetail.html?MN=L32HD31R
The native resolution is 1366x768 which means that it will always display 768p
(which is pretty much equivalent to 720p).
It also appears to only accept inputs of 480p, 720p and 1080i.
No problem there either, unless you try to input a 1080p signal (from blu-ray for example), it will return the message "invalid signal input".