If you are in a domestic partnership under CT law, you will need to go to court to have the partnership terminated. This termination process (akin to a regular divorce) will deal with the division of the assets (called a property division or settlement in a divorce case).
You can certainly sell the house and divide the proceeds however you BOTH choose. That being said, things often go wrong and spending some time with a lawyer will certainly help you understand both your rights and obligations.
As to whether you need a lawyer: the answer is no. That being said, you should (because there is real property involved) retain an attorney to help you protect your interests and help insure you get a fair settlement.