For about a decade, the Watchtower was AFFILIATED with the U.N. as an NGO (Non Governmental Organization). As an NGO they had to spread the word about what good the U.N. is doing, and regularly did so in its Awake magazine.
The Watchtower was never a "member" of the U.N., they were just affiliated as an NGO up until 2002 when MacHislopp's thread on this website and an article in The Guardian newspaper in the UK blew the lid off their involvement with the organization they painted as "the image of the wild beast".
Suddenly in '02 they dropped their membership, stating in a letter to the elders that the inappropriateness of such 'had been brought to their attention'. (By whom ? By apostates and by the exposure in a widely-read newspaper.) They got caught with their hand in the cookie jar.
I don't know as much about the OCSE, but I believe you're right about their involvement. Other posters will likely clarify that.