Adelaide parents accused of the manslaughter of their four-year-old daughter have been granted home detention bail.

Ashlee Jean Polkinghorne, 21, and Benjamin Robert McPartland, 27, of Ingle Farm, appeared in Holden Hill Magistrates Court on Friday.

They are charged with manslaughter by criminal neglect over the death of their daughter in January last year.

They were arrested by detectives on Tuesday after a long investigation by the family violence division.

Their lawyer, Andrew Ey, applied for simple bail, but magistrate Derek Sprod said he was only prepared to order home detention bail because of the seriousness of the charge.

Describing the girl's death as a "tragic accident", Mr Ey said his clients were born and bred in Adelaide, their families were here and they were not a flight risk.

Polkinghorne was due to start a TAFE course on skincare, retail and make-up, while her partner was due to start an engineering course focusing on metal fabrication.

After granting them home detention bail, the magistrate adjourned the case to Adelaide Magistrates Court on March 26.