They should probably look at her facebook.
Does she have a bazillion pics of the kid, is her account just to friends, friends of friends or open for the world to see. In that case, maybe look back and see if they could run down an IP of someone who spent signficant time looking at pics of her kids.....never know.
If they have other kids in the home, it almost would have to be someone they know, an acquaintance of someone they know, or someone they're around with that baby.
Alot of times, aren't these crimes committed by a woman who has recently lost a baby or had a miscarriage?
Some hobo doesn't walk down a neighborhood street, randomly pick a window and take a baby.
"Silence is Golden. Duct Tape is silver"