Whenever any of us cry, excess tears flow toward the inner corner of each of our eyes and enter two tubes called the lacrimal ducts. From our lacrimal ducts, our excess tears flow down a bigger tube called the nasolacrimal duct, which actually opens into our nasal passageway. This is why a "runny nose" can accompany a good crying session. source

In other words, crying causes a runny nose. A congested nose can cause crying, however.