A man has been charged with manslaughter over the death of a four-year-old child in north-west Tasmania.

Hospital staff notified police after the child died in a Smithton hospital about 10.15pm on Friday, May 31.

Police have been investigating the child's death since.

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"Last night a 35-year-old-man from North West Tasmania who was well known to the child was charged with manslaughter in relation to the matter," police said in a statement today.

"A 30-year-old woman from North West Tasmania who was well known to the child is also facing charges.

"She has been charged with ill-treating a child and has been bailed to appear in court at a later date."

The man has been held in custody to appear in an out-of-hours court session at the Burnie Magistrates Court this morning.