Typically, state government involvement in Social Media has been either:
1. In the form of public diplomacy, with a state sponsoring or endorsing activities in which it’s citizens engage with those of others such as student exchanges.
2. Glorified news-feeds, with the “news blast” style of using twitter
3. Governments co-opting social media to monitor and quell uprisings and activists (like Iran during the Green Revolution).
There’s very direct tit-for-tat engagement between official state players though, which for me is what piqued my interest reading the reuteurs release of diplomats going at it on twitter. Shorter version; US Ambassador to Russia, Micahel McFaul, tweeted concern about the arrests of peaceful demonstrators, and the Russian Foreign ministry replied on twitter. Seems mundane I know, and perhaps it’s because I’m not on twitter enough, but my sense is you don’t (yet) see this kind of engagement on social media between diplomats.
See the Reuters story here: http://www.reuters.com/article/2012/03/06/us-russia-election-usa-idUSTRE82510Q20120306