Sorry no, Trulia does not allow for-sale-by-owner listings on their site. They say that this is a means to cut down on spammers.
I suggest that you post your home on Zillow.com or Craigslist.com as you can do so for free. However; your home will get the greatest amount of exposure on real estate websites if you list with a real estate agent who has a lot of marketing savvy. Just food for thought...
Prudential Connecticut Realty