There was no such thing in the first century of Christianity. There were many Christian churches/congregations that acted autonomously, though still part of the Christian movement. Bishops and deacons were set as the head of each local church, though they probably did not have as much 'power' as a modern day church leaders. They were more of an overseer of the church, being educated they could read for the church and make general decisions.
A good example of how this played out was the forming of the New Testament canon. Each congregation had various books that they saw as fitting into the new testament, some accepted only certain new testament books (synoptic gospels and a few of Paul's epistles) or books that are not longer in our canon like Apocalypse of Peter, Didache, or Shepard of Hermas just to name a few.
The first Bishop of the Roman church, Clement of Rome was appointed by the apostle Peter. Clement, spoke much about Christ and quoted a few well know saying of Christ, which are found in the synoptic Gospels. When writing a letter to Corinth he encouraged the people there to read from Paul's letter to them. However he made no mention of any of these New Testament writings as being scripture, as he did with the books of the Old Testament. For Clement, though he was a Christian, scripture was only the Old Testament. Though, other church leaders like Papias, who was a successor of one of Apostle Paul's workers Epaphras, did see the written word of the New Testament to be of great importance and often quoted from it. There were several others that held this same opinion such as Polycarp of Smyrna. So, you can see a variance of opinion in the first century church leaders, though they were both part of the Christian movement.
The 'Christian' books that are not in our canon today were largely written after the first century, but still some of these came to be respected and held as scripture and canonical. Clement of Rome wrote his own epistle and it came to be respected and even included as scripture in some churches around the third century. Shepard of Hermas enjoyed canonical status in many churches and was even listed as scripture by Eusebius along with the Epistle of Barnabas. One book that lingered in the New Testament longer than any other was the Epistle to the Laodiceans which was still viewed as scripture in 1165 by John of Salisbury, though most of the church rejected it. In exception to Laodiceans, the canon was closed by Augustine between the years 397-419, when he made an official list (to be held by all Christian churches) of the 27 books of the New Testament and did not hold any other books to be scripture.
That was a bit long to make a point, but it shows the type of Christian organization there was in the first few centuries. If there was a central governing body, like that of the JW's, they would have come out with a list of official New Testament writing and sent a letter to all the churches. Nothing like that ever took place. Instead, there were individual churches that had various opinions as to what was to be regarded as scripture. If there was a governing body like the JW's, it would have not taken until the early fourth century to have an official list of New Testament books. Imagine there was something like a JW governing body in the first century, but they could not even muster a letter to all congregations of which books were to be considered scripture.....not very likely.
A governing body did not come about until Christianity was legalized by the emperor Constantine in the early fourth century. It would have been impossible for there to have been a centralized body before that point. The Christian church was persecuted and by necessity had to act autonomously. It would have been far too difficult to have a central location from which all instruction was sent. Any central location would have been easily known and attacked. There was simply nothing like a JW governing body in the first, second or third centuries of Christianity.
