As a noun, capital refers to (1) a city that serves as a center of government, (2) wealth in the form of money or property, and (3) a capital letter. As an adjective, it means (1) principal, (2) involving financial assets, and (3) deserving of the death penalty. There are other definitions of capital, but these are the most commonly used ones.
Capitol has two very specific definitions (outside ancient Rome): (1) a U.S. state legislature building, and (2) the U.S. Capitol building in Washington, D.C. State capitols are located in the capital cities of U.S. states, and the Capitol is located in the capital city of the U.S. If you’re not talking about any of these capitol buildings, then the word you want is probably capital.
The Capitol building located in Washington, D.C. is spelled with a capital C, but state capitol buildings ordinarily don’t have the capital C (which is not to say that some writers don’t capitalize them anyway).
The ability to expand depends on access to capital. [Capital Spectator]
Wilderness — with a capital “W,” according to the Wilderness Act — offers the values of “solitude,” and “primitive, unconfined recreation.” [New York Times]
The House will take up a bill this week adding one statue of a District luminary to the halls of the Capitol. [Washington Post]
In 1972, the U.S. Supreme Court banned capital punishment, but the decision was overturned in 1976. [Columbia Missourian]
You are a capital fellow, Planchet. [Ten Years Later, Alexandre Dumas]
What it does have is the state capitol building, Vermont State House, with its impressive gold leaf dome backdropped by the wooded hills of Hubbard Park. [Guardian]