Here is a map on how US state capitals are ranked by population in each state.
Check this Wikipedia entry for the source of data.
States with most populous city as state capital:
Idaho, Wyoming, Utah, Colorado, Arizona, Oklahoma, Arkansas, Iowa, Mississippi, Indiana, Ohio, West Virginia, Georgia, South Carolina, Massachusetts, Rhode Island.
States with 2nd most populous city as state capital:
Oregon, North Dakota, Nebraska, Minnesota, Wisconsin, Louisiana, Tennessee, Alabama, North Carolina, Delaware.
States with 3rd most populous city as state capital:
Alaska, New Hampshire.
States with 4th most populous city as state capital:
New Mexico, Texas, Kansas, Virginia, Rhode Island.
States with capitals not among the top four cities by population:
Washington, Nevada, California, Montana, South Dakota, Missouri, Illinois, Michigan, Kentucky, Florida, Pennsylvania, Maryland, Delaware, New York, New Jersey, Vermont, Maine.