We have a few sides to this story:
- Israeli citizens
- The Israeli Army (IDF)
- The Gazan citizens
- Hamas, the rulers of Gaza
- Independent journalists who are not Israeli or Gazan
The location in question is right in the middle of the Gaza strip and both sides would likely fire over that point. It should be noted that a significant portion of Hamas weapons, being improvised, fall short of their intended targets and land in the Gaza strip. Consider this incident in which a three year old Gazan girl was killed by a misfired Hamas rocket. Therefore, either side could plausibly have fired the projectile which landed in Shifa.
Israeli citizens have no evidence one way or another, they were not present so I do not see their viewpoint as being significant.
The Israeli army
The Israeli army, as party to the conflict, would be a likely suspect. The IDF denies that they fired on the hospital, and in fact blames Hamas. That is not surprising, I'm not sure of any incidents in which the IDF said "yes, we bombed that place that we shouldn't have".
The Gazan citizens may or may not have seen from where came the projectile, or from where it was launched. I have not seen any reports from Gazan citizens regarding this specific incident. I speculate that is because if it was an Israeli projectile, then it would have been moving too fast to see from where it came, and if it were a Hamas projectile then whoever saw the launch would not know to correlate it with the hospital, and whoever saw the explosion would have no way of knowing from where it came. I don't know if Gazan citizens would keep quiet out of fear if they knew it were a Hamas projectile.
Hamas claims that the missile is Israeli in origin. This claim is supported by the fact that Hamas uses the hospital as an operation center and launches rockets from the hospital, thus one would conclude that would make it a military target for the IDF.
An independent journalist has reported that the missile which hit al-Shifa was a misfired Hamas missle. However, by the same reasoning that Gazan citizens would not know who is responsible, I don't see how the journalist could conclude that Hamas was responsible. His explanation for his conclusion is
Witness: militants rushed and cleared debris which seems tentative at best.
Either side is plausible. People will believe that "the other side" is responsible no matter which side of the conflict they are on. With no remains of the projectile saved to be examined, we will probably never know.
What evidence does remain
This is a late edit. I've found the following photograph which purports to be the site of the bombing. I cannot say if it is accurate or not. Perhaps someone familiar with the types of weapons used by Hamas and Israel could make an assessment.