Are you thinking of Nebraska, which has a unicameral legislature? That means there is only one house. Every other state has two houses, just like the US Congress. The upper house is usually called the Senate, but the lower house may be called the Assembly (in NY), the House of Delegates (in VA), or whatever.
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The California legislature has so much work that it meets continuously for each two-term session. Most State legislatures hold annual legislative sessions; they meet for several months every year and then adjourn. A few legislatures still follow the old practice of meeting every other year, but this system has become less practical as legislatures have become busier.
Arizona's Legislature meets annually. Up until 1950, it used to meet twice a year. The Arizona State Legislature was established in 1912 when Arizona became a state.
Nebraska is the only state with a nonpartisan state legislature today.
State legislature
Nebraska is the only state NOT to have a bicameral legislature. Instead, the state has a unicameral non-partisan legislature. This means that there is one house instead of a house and senate.
Nebraska