Indiana Code Title 16. Health § 16-36-2-3

(1) By the surviving spouse.  However, if the deceased and the surviving spouse were legally separated at the date of death, the survivor is not considered a surviving spouse.

(2) If there is no surviving spouse, then by any one (1) adult child of the deceased.

(3) If there is no surviving spouse or adult child of the deceased, then by one (1) parent of the deceased.

(4) If there is no surviving spouse, adult child, or parent and there is an adult who is next of kin of the deceased residing in the county in which the deceased died a resident, then by any one (1) next of kin.

(5) If there is no surviving spouse, adult child, parent, or next of kin, then by any person assuming custody of and financial responsibility for the burial of the body.