In agreement with above, the Bible says the Law is written in our hearts, but that is the Law of the Book of Nature, which one can 'read' and comprehend by the contemplation of nature, and does not require Divine Revelation to be evident.
So in answer to your question, no, one does not need a belief in a deity to be a moral person.
The highest moral law, the Golden Rule, "Do unto others as thou would have them do unto you" is not a Revealed dictum in any religious tradition – rather it is implicit in all of them, which attests to its universality.
As I see it, the Decalogue, the Ten Commandments, only the first three (in the Catholic numbering, traditions vary) are revealed by God – the remaining seven are cultural moral values common in the region at the time and not unique to the Jews:
1: I am the Lord thy God, Thou shalt have no other gods before me, Thou shalt not make unto thee any graven image
2: Thou shalt not take the name of the Lord thy God in vain
3: Remember the sabbath day, to keep it holy
4 Honour thy father and thy mother
5 Thou shalt not kill
6 Thou shalt not commit adultery
7 Thou shalt not steal
8 Thou shalt not bear false witness against thy neighbour
9 Thou shalt not covet thy neighbour's wife
10 Thou shalt not covet thy neighbour's house, wife, his slaves, or his animals, or anything of thy neighbour
So I would say 1-3 are Revealed Laws – one might well argue common sense (1: Believe in God, 2 and 3: Don't upset Him)
4-10 are moral codes broadly existing across the region in the time in question, and again, near universal as societies emerge – basically to protect the weak and curtail the strong. Here they receive divine endorsement, but God did not come up with them on the mountain.