This basically translates into a government wherein the powers of the central (national) government are limited or restricted and in which the component states enjoy a certain degree of autonomy, sovereignty and self-government. In this form, the sovereign power rests with the people who elect their representatives. However, the component states that form the United States are bound by the Supreme law of the land, the Constitution.
With that in mind, it would be necessary to state the degree of autonomy each state has in governing its respective territories and constituents. Each state has the three main branches of government, namely the executive, legislative and judiciary. The executive is headed by the Governor, while the legislative and judiciary are composed of State representatives similar to that of these branches at the national level. Each state has its own laws and each State Supreme Court has the power to create the judicial determination of issues of law on their own, subject only to the limitations imposed by the Constitution and the US Supreme Court.
One of the limitations imposed by the U.S. Constitution on the issue of capital punishment is mainly enshrined in the Eighth Amendment, prescribing the use of cruel and unusual punishment. For around four decades now since 1976, the U.S. Supreme Court has held steadfast in its ruling that the death penalty does not violate the Eighth Amendment. Another key limitation is one wherein the U.S. Supreme Court overturned death penalty sentences in 19 states when it held that the death penalty could not be imposed on convicted murderers who were under the age of 18 at the time they committed their crimes. (Walker 2006)
Thus, it can be seen that indeed each state has the right to determine whether or not a convicted felon should be executed, as long as the State law allows it, and the practice is in accordance with the limitations set on the National level.
Therefore, various differences can be seen as to how State practice and legislation allows capital punishment.