Unlike the class $P$ or $NP$ the class $NC$ does not have any complete problems. To show a problem is in $NC$ one needs to marshal efforts to directly show the problem is in $NC$ since there are no complete problems.
What are some of the known techniques to show a problem is in $NC$?
For example reducing to determinants is one way since there is an $NC$ algorithm for determinants. Every attempt to show perfect matching is in $NC$ is through a reduction to determinant by derandomizing isolation lemma.