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I have a student who is looking for annual data for each state on the party composition of their state legislatures, specifically the percent of Democrats in state legislative chamber.
ICPSR Study 16: Partisan Division of American State Governments, 1834-1985 should have the information your student needs. It includes both the number of legislators from each party for each year and percentages.
After 1985, the Book of States, which is an annual publication produced by the Council of State Governments, has this information. There is a pdf version that covers the years 1973-2003, which has the specific information the student needs and is cheaper than each individual volume.