Conrad Murray has sued the State of Texas to win back his medical license.

As you probably know ...the Lone Star State took swift action after the whole Michael Jackson thing and yanked his license for good in August of last year.

TMZ first reported ... the doc will challenge both Texas and California for putting the brakes on his ability to practice medicine.

Murray clearly needs something to do to earn cash.  In the docs he filed ... Murray says he's more than $400K in debt and can't even afford to pay court costs.