The three-month-old girl died after emergency services were called to reports of a child in cardiac arrest in woodland off Strawberry Lane, near Cheslyn Hay, at 08:45 BST on Saturday.
The people arrested were a 42-year-old man and 30-year-old woman from south Staffordshire, a 20-year-old woman from Wolverhampton and an 18-year-old man from Walsall.
All four were detained at the scene and have since been bailed while inquiries continue, Staffordshire Police said.
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