William Shakespeare was himself Christian, writing to an audience which was Christian, in a period and location where Christianity, in the form of the Church of England, was the official established religion of the land. Thus it is legitimate to interpret Hamlet from a Christian perspective.
There are two directions one could explore from a Christian perspective. One would be a discussion of whether the ghost is really the spirit of Hamlet's father seeking justice or a demonic apparition tempting Hamlet to commit matricide and condemn his soul to damnation. The interpretation of the ghost as a portent also seems to raise the question of pagan superstition vs. Christian piety. The initial reactions of the characters to the appearance of the ghost suggest these question, e.g.:
A little ere the mightiest Julius fell,
The graves stood tenantless, and the sheeted dead
Did squeak and gibber in the Roman streets;