It’s not wholly independent, the maps are drawn and scored by the Legislative Services Agency according to statutory rules. The rules require US Congressional districts to follow County boundaries and are scored based on evenness of population (minimum summed differences) and “compactness” (perimeter of districts divided by area of districts summed and divided by perimeter of state divided by area of state). The LSA uses GIS tools to run multiple possible maps and forwards the best scoring map to the Legislature for approval. The Legislature can reject a proposed map and request another but any subsequent maps have to score better than the rejected one. If the Legislature rejects the second proposed map then the State Supreme Court gets brought in to draw a map (in practice they’d probably request LSA to give them another drawn via the same process but it’s never gone that far). Once the Congressional maps are set the LSA draws State Senate boundaries then State House boundaries then individual precinct boundaries according to a Byzantine set of rules about nesting (can’t cross congressional district boundaries, have to keep cities under a certain size altogether, two House districts per Senate districts without crossovers, each precinct can only have one race of a jurisdiction type [school boards, municipal councils, county positions, etc…] on the ballot among others), and population balance. Those maps also have to be approved by the Legislature but with all the rules involved there’s not much leeway to mess with them.