[Ursus Maior]

That would not have been a decision, in theory, to have been made by the German government. The defense of Germany was fully integrated into warplanes of NATO and that included the use of nuclear weapons. All of this was controlled by NATO and the armed forces or states that had (some or all) of their nuclear-armed weapons assigned to NATO. So, it would have been NATO's military component that would have ordered the use of nuclear weapons, but of course a political process would have taken place before that decision would have been made. That political process would have taken place in NATO's political structure.

There were two important exception to this rule concerning your question, though. First, France had left the integrated military command during the 1960s, but had remained a fully committed member of NATO on the political level. Second, Germany, under the Bonn–Paris conventions had regained "the full authority of a sovereign state" in 1955, but that sovereignty was in fact somewhat limited and revocable by the Western Allies. And while all armed forces in Europe were fully integrated into NATO (sans the French forces during peace time), Germany had somewhat lesser rights. Also, Germany retained the Territorialheer, its territorial army, distinct from the Feldheer, the regular army. The Territorialheer was not part of NATO's integration (in theory), but only Feldheer units were to be equipped with nuclear weapons from US-German joint depots in wartime.

The Feldheer was structured up to corps level (plus a slim national command structure during peacetime), with all higher command functions being part of NATO. This was how NATO worked. Should NATO consider the use of nuclear weapons, the first question would be "what's the context"? E. g. nuclear weapons could already have been used strategically and by one or both sides. Second, nuclear weapons could be used first by NATO on a tactical level to destroy breaking through Pact (likely Soviet) forces. Third, Soviet forces could have already used nuclear weapons on a tactical level, disrupting - amongst other effects - communications with parts of NATO's leadership.

Most likely, NATO's intelligence apparatus and those of its members would have seen the use of nuclear weapons coming. Taking nukes out of their shelters, priming them, readying them etc. shows up on satellites and other intelligence sources. In that case, talks would have been held. What happens, if they fire first? What if the German leadership or indeed NATO's political leadership is killed off or disrupted and cannot decide in time to retaliate etc.

In the end, plans would have been made in advance, to make sure they can be played out when necessary. Improvising during wartime is bad, improvising nuclear war is just suicide. And the plan during the 80s was always: nuclear weapons are an actual option for various scenarios. So, if push comes to shove, would Bundeskanzler Helmus Kohl have ordered it? On West German ground: probably, but depending on the "where" maybe not. Chancellor Kohl was from Rhineland-Palatinate. He might have hesitated to nuke Frankfurt and the rest of Hessia. I'm not sure, he would have spared Bavaria, save for Munich maybe. But glazing some small towns in the great northern flatlands? I'm convinced, he would have done it.

On East German ground? Absolutely, yes! Until 1989 reunification was a distant, abstract goal. The Cold War was a total war of two systems. West Germany wanted to build a nuclear repository (the final resting place ouf our burnt out nuclear waste) right next to the Inner German Border, well aware that it might seep into East German ground water. Politically, no quaters were given and if it would come to the point of "us or them?", raining death onto a concentration of Soviet divisions, about to pour into Hamburg? Sure thing. He might have hesitated to do the same to East German divisions, given the option to "either 3 Soviet division or 3 East German ones", but again: total systematic opposition. The right-wing of Germany, including Kohl's party CDU, was famous for its battlecry of "dead before read" ("lieber tot als rot"), meaning they would have chosen to die, before submitting to communist rule.