Are there anyone from the Rawls or Ralls surname that can tell me anything about the history of their family?

http://wc.rootsweb.com/cgi-bin/igm.cgi

had 13,500+ entries if you leave everything blank and enter just the surname Rawls. I didn't try the RALLS spelling. I didn't limit the search to those born in Connecticut, either. You could. Use the two-character postal abbreviation in the birth, death or marriage place. (CT, TX, PA, etc.)

You won't find your parents, but you might find your grandparents or GGP's. Genealogists limit themselves to dead people. If they post living ones, they post just the last name. You could try the given name "Living" and the surname "Rawls" to see if any of the spouses look familiar. If your dad was a Rawls and your mother a Jablonski, search for living Rawls with Jablonski in the spouse field. If you don't get any hits, try with your grandparents Rawls and his/her spouse.

Depends what you are looking for. Try www.familysearch.org or (look for a local center using the site). There are also other sites to use to locate info on this family history.