Matthew 27:64

“Command therefore that the sepulchre be made sure until the third day, lest haply his disciples come and steal him away. And say to the people, ‘He is risen from the dead,' and the last error will be worse than the first.”

So they requested that Pilate, who had overall responsibility for the body, should secure the tomb in which Jesus' body was lying, guarding it for three days in case His disciples came to steal it away and then tried to pretend that He had risen. Once the three days was over they could then if necessary prove that such a thing had not happened by producing the body. Let him consider what the disciples would be able to do if they were able to steal the body. They would be able to claim, ‘He is risen from the dead'. And that would simply compound the ‘deceptive error' that Jesus had been declaring, that He was the Messiah Who would arise from the dead.

The Chief Priests would have known that they had no right themselves to set their own guard over what was Roman property (the body of Jesus), at least, not without permission. It would have made Pilate look as though he was being incompetent. And the tomb itself was a privately owned one, belonging to a respectable councillor. They would not themselves therefore have wished to cause offence by putting on an unofficial guard.