The primary examples of communism (USSR, China, Cuba, Venezuela) have at their head a very strong central authority which approaches if not is in fact a dictatorship. Are there any examples showing that it is possible to have a communist country that has free and fairly elected leadership or other non dictatorial governance?
Yes. You could conceivably have a democratic communism.
Communism is an economic type not a government type. Communism is simply a system of non ownership and shared resources for a group of people, in this case a nation. You could have a nation that agrees that no one owns or has anything other than a temporary possession of any thing. That any item including the home that you built and have taken care of can be reapportioned to someone else just on the vote of a majority.
I would note that many so called communist countries (China, Russia, Venesuela, Cuba) are actually Socialist Marxism.
I believe it more accurate to say that pure communist governments are more prone to facilitating dictatorship, with their single party, lack of general elections, and state control of just about everything. In the communist countries, the party runs everything. With the government dictating everything, it is a lot easier for a genuine dictator to take over, than it would be in the democratic nations.
It may also be accurate to say that dictatorships appear more like communist countries, with the dictator running everything.
A communist government is just another political government. In fact, communism is an ideology. An ideology does not make a government and hence a dictatorship, but rather dictates the governments point of view on politics and how things are done.
This said, communist countries tend to be or at least to become a dictatorship at least per se, even though they might have elections. However, it is not a mandatory step. Theoretically, a country could follow the ideology of communism, while still having an elected government. It works the same way on the opposite side: you can lead a fascist government while still not being a dictatorship.
Issue is, that most such governments tend to make changes to laws or to decrete restrictions, which at least limit democracy or lead to a full dictatorship.
But to answer your question: at least theoretically you can be a communist, fascist, etc. country, without being a dictatorship as communism is just an ideology, not a form of government.
On the other hand, there are right now just four communist countries left... North Korea, Cuba, Vietnam and China. There is not much to say about North Korea, as it is a dictatorship... so is Cuba, though it is opening. China on the other hand, while it does have many restrictions and limitations, is not a dictatorship.
In the general form in which the question is asked, yes, under some specific conditions.
As an example, take some theoretical communist state which exists in Star Trek like post-scarcity technological development state, with near infinite cheap energy and near-free material goods up to an including some luxury ones.
In such a system, theoretically, a majority of population would be content enough that they would not need to be oppressed to vote for the "right" leader who agrees with the system, as they would not want to change the system. So free elections would not be a problem to system's stability, as they are in scarce economic conditions where people are NOT happy to live in socialist "paradize" which in reality sucks.
Pre-oil-crash Venezuela would be the closest practical example I can think of - while Chavez was a dictator, he WAS immensely popular due to bribing his population with material wealth from export of expensive oil; and thus was widely popular; and I suspect would have won free and popular elections. Until oil revenues fell.
A community that's packed by design with people who stably hold to the communist system (for example, for religious reasons) would also theoretically be able to sustain free elections - throughout history, people are willing to tolerate pretty bad poverty with no tyranny forcing them if they do it for religious reasons.
Frankly, I find it difficult to come up with a historical example (the best such examples would be Oneida or Münster Anabaptists; but they came built in with the authoritarian top dogs and no elections; from the start so couldn't serve as experiments to test this theory).
"USSR, China, Cuba, Venezuela" aren't communist countries. They were socialist ones, and socialism is a dictatorship by definition.
I decided not to mention Sweden, since Nordic model isn't even fully Socialist per se, never mind communist.