Norm-
I'll have to go out to the coach to confirm my model number, but our LCD is a 2006 build like yours, and that Sharp number sounds familiar, though ours is a 32", not a 37".
I had to hook in a converter box in 2007 or 2008, since our TVs do not have a built-in digital tuner (ATSC) like most built only shortly after '06. As I recall this summer in Canada I didn't need to turn the converter on; I presume they must still broadcast a lot of analog (NTSC) format. Unlike yours, the Sony in our bedroom is an LCD, not a CRT.
Regardless, I'd like to one day replace one or both units with 120Hz multi-tuner TVs; the 60Hz refresh rate is like watching action scenes or facial close-ups through a fish bowl, and the converter boxes are an inconvenience and another heat source in a tight enclosure. A more contemporary 1080i/p HD resolution would be nice too; 720p is just not up to snuff for today's movies and HD content.
Joel
ps . Like ours, your TV has only an analog tuner, NTSC. Note the specs, "Video Standards" here:
http://www.webmall2000.net/home/37hv4u.asp