"My baby is sleeping in the crib."

Translation: Mein Baby schläft in der Krippe.

[rmz]

Why can't I write "Mein Baby schläft im Krippe" ?

[wataya]

You might want to have a look at this discussion http://duolingo.com/#!/comment/10694 concerning the meaning of 'die Krippe'.

[Menschenkind]

No. im = in dem. dem is used for masculine objects; Krippe is feminine.