The only Warsaw Pact country that to my knowledge (which is limited on this) had any kind of nuclear program was Romania. I don't know much about the details, unfortunately, but they apparently had an exploratory and ambivalent nuclear program in the late 1970s that maintained an interest in weapons. They were an odd country in the Cold War, because they were in the Warsaw Pact but also did things their own way at times, including negotiating with the United States for (highly-enriched!) nuclear fuel for their research reactors. (The US gave Romania a total of 38 kg of HEU, which is enough to make a bomb if you know what you are doing.) The USSR had at one point promised to base nuclear missiles there but declined after the Cuban Missile Crisis.

My guess is that if the USSR knew about any nuclear program that had a chance to get off the ground it would have worked to shut it down or sabotage it. The only role such a nuclear program would have from their point of view would be to decrease Soviet freedom of action. They learned a hard lesson from China in the early 1960s in this respect.

The only articles I know of on this topic are by Eliza Gheorghe, and my information in the first paragraph above comes from her article "Atomic Maverick: Romania's negotiations for nuclear technology, 1964–1970," Cold War History 13, no. 3 (2013).

Czechoslovakia has had a nuclear power program with its roots dating as far back as 1956, but its purpose was strictly civilian. That being said, there are claims that nuclear weapons were based in the country during the Cold War not only in the hands of local Soviet units, but also possibly available to Czechoslovak armed forces in case of the conflict turning hot.

In 1956 the decision was taken to build a nuclear power plant in Jaslovske Bohunice in present day Slovakia, using a Soviet designed reactor built in Czechoslovakia, the KS-150. The construction of the plant started two years later in 1958, but it would not be finished until 1972 and even then it continued to be plagued with problems, having had to be shut down several times during its operation, including a level 4 accident on The International Nuclear Event Scale ("accident with local consequences"), and providing negligible energy output.

Following these issues, the KS-150 facility was shut down in 1979, but nuclear energy was not abandoned. In fact, in 1970 a contract between Czechoslovakia and the Soviet Union was signed with the aim of building two nuclear power plants using the newer VVER reactors – one an expansion of the existing Jaslovske Bohunice plant (two blocks between 1980 and 1981, and two more a couple of years later), the other a new facility in Dukovany (first of four blocks finished in 1985).

Between 1979 and 1982 plans were drawn and work started on two more projects, the Temelín and Mochovce nuclear plants – in present day Czech Republic and Slovakia, respectively – but these would only be finished after the overthrow of the communist regime and the following split of Czechoslovakia, mostly due to financial and political difficulties and constraints.

Now as for the issue of military application of nuclear power, things get a bit more difficult. The Czechoslovak army possessed nuclear-capable launchers since the late fifties, and a series of agreements from 1965 onwards between the two countries did specifically provide for designated nuclear ammunition warehouses and more launchers, including 9K52 Luna-M and R-11-M (Scud), to be built and stationed in Czechoslovakia.

There appears to have been some disagreements between the two sides as to the control over these assets, but the 1968 Warsaw Pact invasion solved them. The munition bunkers were placed under direct Soviet control, as would any potential nuclear weaponry supply. Furthermore, at some point in the early 1970s, Soviet forces deployed at least two nuclear rocket artillery regiments to Czechoslovakia.

After the Velvet Revolution and the withdrawal of Soviet armies, Czechoslovak authorities conducted radioactivity measurements at these sites to find out whether the local Soviet forces were in possession of nuclear weapons. The results suggested no warheads were present.

However, in 2007 historian Petr Lunak claimed that the opposite was true, not only because heavily shielded nuclear ammunition would leave few or no traces of radioactivity. According to his research and eyewitness accounts, the army staff had knowledge of nuclear weapons stored in Czechoslovakia and actually planned some 130 strikes in the event of a war – in which the Czechoslovak forces were tasked with an advance through southern Germany towards Lyon, France – and it was in fact the Czechoslovak side which actively clamored for access to nuclear weaponry in order to achieve their objectives, as opposed to Moscow simply stationing troops under its direct command locally.

Now Lunak is not some looney conspiracy theorist, he has worked in some capacity at NATO, but his claims were opposed by for example the first post-1989 minister of defense Miroslav Vacek. And although his study does include several previously secret documents and plans suggesting he might be correct, such as the Lyon plan which apparently would not be feasible without the use of nuclear weapons, we still do not possess definite proof of nuclear weapons in Czechoslovakia.