Britney Spears and Kevin Federline have some unfinished business ... they owe more than $37 GRAND to the State of California ... this according to official docs obtained by TMZ.

The CA Franchise Tax Board just hit the former couple with a $37,712.71 lien for unpaid income tax from 2004 -- the same year they tied the knot.

FYI -- Britney made a TON of cash in '04 from a concert tour and a very successful greatest hits album ... while K-Fed appeared in "You Got Served."

The lien shouldn't be a problem for Britney -- she's loaded these days. K-Fed on the other hand, he ain't exactly drivin' Ferraris anymore.

A rep for Britney tells TMZ, the lien was filed in error and will be rectified soon. No word yet from Kev's people.