Does anyone know specific laws or procedure to arrest someone for child abuse or neglect.?

you don't say where you are in the world. But in the uk i would report your concerns to the police as has been said before. I'd imagine they may then liase with ohter childcare organsiations who may investigate to see what action including possible extra support for the mum is needed. Ask the police if thats what they do and if not ask then for advice on what ohter childcare orgainsations such as the NSPCC to report to it.