(a) Not later than the 10th day after the date of a death that occurs in this state, a death certificate shall be filed with the local registrar of the registration district in which:
(1) the death occurs; or
(2) the body is found, if the place of death is not known.
(b) Subject to department rules, a certificate of a fetal death that occurs in this state shall be filed with the local registrar of the registration district in which:
(1) the fetal death occurs; or
(2) the body is found, if the place of fetal death is not known.