Boris Shor and Nolan McCarty have produced a graph showing the polarization of the states compared to Congress. It's seems clear enough that polarization is a real problem in many states but breaking down ideology at the state level has proven tricky. As Shor points out:

…each state in its own way is rather unique. Massachusetts Republicans aren’t the same as Texas Republicans; the same is true for each state’s Democrats. Nor do they vote on the same things.

Eyeing the graph it appears that around 30 states are either equally polarized or more polarized than Congress. Worth noting is that ideological polarization does not necessarily translate into gridlock. The key in-grid-ient is party parity; e.g., California is polarized to a degree that our hyper-partisan Congress can't hope to match but because Democrats dominate so thoroughly the government works..at least according to Democrats.

Be that as it may we must bid Shor and McCarty safe traveling as they venture forth for the Rosetta Stone of state polarization:

All in all, polarization varies fairly dramatically across states.  The natural question is: why? Nolan McCarty and I–along with some coauthors–are engaged in a number of different research projects to try to answer that very question, as are a number of other scholars.