If the so-called resurrection were really subject to a serious investigation, there would be major doubts as to whether it really occurred. First, it would be one of the most significant events in history (and according to many people, it is the most significant event in history), yet it escaped the notice of all but a few. Perhaps this was due to the fact that phony resurrection tales had been floated before, but there was no proof for them.
Second, the accounts in the Bible disagree in almost every detail. Who went to the tomb? Was the tomb sealed? Were there angels present? If so, how many and where were they? Was Jesus himself there, alive in some form? Was anyone told afterward about the discovery of the empty tomb? How many disciples ran to the tomb to check it out? About all the Gospels agree on is that Jesus had risen. But there is a very serious lack of "getting the stories straight," which indicates that (at best) none of the accounts is first-hand and that no one really knows what happened. Even taking the resurrection accounts at face value and ignoring all the conflicts among them, there were no witnesses to the actual resurrection event.
Third, according to the Scriptures, there were early murmurings that there had been no miracle at all. The book of Matthew reports that those crafty folks, the Jews, bribed the guards to say that the disciples had stolen the body. Even if this bribery story is nonsense (as it probably is), there are plenty of non-miraculous explanations for the event.
Fourth, at least three Gospels report that people who knew Jesus personally were not sure that the person they saw was the resurrected Jesus. When people who knew the deceased best supposedly see him resurrected, but are not satisfied that the person they saw is indeed their deceased friend, then serious doubt is cast upon the resurrection story. (Up to a few centuries ago, it was not uncommon for imposters to try to assume the identity of influential people who had died or been executed. One way to deter imposters was to display the body publicly for a time, so that people could be assured that the real person in question was dead.)
Now, none of these things means for sure that the resurrection story is false. What they do mean is that there are legitimate questions about the credibility of the reports. Any truly serious investigation would have to address the credibility problems.