on a personal note, i do not think governments invest in bitcoins secretly because it's a decentralized peer to peer transaction with no central authority and also it can affect the country's fiscal policy, business and also help to facilitate crime rates.
the government may not invest in bitcoin, but the banking world of a country can invest in bitcoin, because bitcoin is a digital currency that can be owned by anyone, so bitcoin investment is global and personal.
what is common is that the government provides various supporting facilities from bitcoin, because the government can withdraw taxes from several facilities provided by the government.