Capitalize the court’s full name

Warning²Federal courts, Illinois courts21st and 22nd editions

A court named in full takes capitals on the court’s own words, as in “the California Supreme Court”; the generic “the state supreme court” names no court and stays lowercase.¹

1. 1R. 8(d)(ii) Exceptions; R. 8(c)(ii) Exceptions. Tables: T10.1 U.S. States, Cities, and Territories.
2. 2A warning: the form is usually wrong under the rule in note 1, and context can justify it.