Legal Question in Constitutional Law in Connecticut

Generally, no. You can use deadly force to protect yourself (or third persons) from the unlawful exercise of deadly force. In some jurisdictions you can use it against somewhat lower thresholds of unlawful force, or even in the defense of your home. But you can't use it to protect, say, your right to due process of law or to free exercise of religion.

Note that most Constitutional "rights" are really just limitations on the power of the government. If a private individual tries to prevent you from, say, attending the church you want to attend, then he is not violating your constitutional rights even though a government official would be if she did the same thing.

Most unlawful exercises of deadly force are done by private parties, not by the government. So when you use deadly force to fend off such an attack, the rights you are protecting are not constitutional rights -- though you seem to assume they are. These rights are very important, but they don't come from the constitution.