The Soviet Union had a central bank, Gosbank which basically ran the economy; it paid wages, stored savings, issues business and personal loans, ran state lotteries and ran as a traditional central bank regulating the economy through fiscal policy.
However the bank was not independent from the Soviet government as in many cases was an extension of policy. Accounts were checked to see if businesses were making what they claimed during the five year plans and loans were often used as rewards to favoured businesses or people.
However this came to an end during perestroika where gosbank was split up into several different banks specialised around various roles, personal savings, trade, agriculture and construction. Some of these survived the fall of the soviet union and continue to exist until this day.