Soviet defector Oleg Penkovsky, active approximately a decade before you are asking, said: "... The employment of atomic weapons will be the decision exclusively of the Central Committee of the Communist Party through the Ministry of Defense." This implies that it was simply a majority vote of a sub-committee of the Central Committee.

Sources:

Penkovsky, Oleg. Lt. Col. Oleg Penkovsky: Western Spy in Soviet GRU. CIA Freedom of Information Act Electronic Reading Room. Meeting 5, Paragraph 91.

And in contrast, what was the reverse?

How many people in the US had to agree?

Piggybacking on this, how many people at a given Soviet launch site were needed to arm the warhead/fire the weapon? IIRC the captain and political executive officer of missile subs both had to turn launch keys, but what about land based Strategic Rocket Forces?

I don't know about a first strike, but a retaliatory strike could potentially have been launched by a relatively junior officer, based on standing orders from their central military apparatus. I haven't read the book "The Dead Hand: The Untold Story of the Cold War Arms Race and its Dangerous Legacy" by David E. Hoffman, but it was about a Soviet system called "Perimeter," also called "Dead Hand," which was a system meant to retaliate in the event of the destruction of, or at least communications cut off from, the central military apparatus in Moscow.

All I've got to link to is wikipedia's description of Dead Hand/Perimeter based on the book, and I know that's not really bueno here, but one should really read the book to get the picture.

If you are interested in the Soviet nuclear (and chemical/biological) weapons program I would HIGHLY recommend The Dead Hand by David E. Hoffman. The Soviets had planned to make an entirely automatic "fail-deadly" missile counterattack system, but cooler head prevailed and they inserted three duty officers that would decide to strike back if certain conditions (inability to reach command, radiation levels etc.) were met.

Additional question: is there historical evidence of anybody with nuclear vote authority in either US or USSR governments trying to make a nuclear attack happening?

Nuclear control was in the hands of the Defense Council, which was an organ of the Central Committee of the Communist party.

The Defense Council consisted of the General Secretary, Premier, Defense Minister, KGB Director, Chief of the General Staff, Minister of Internal Affairs, and chairman of GOSPLAN.