For your information, live crabs falls under the category of Seafood Items.
You are allowed to bring in the mentioned item to Singapore for personal consumption, provided that the total quantity of seafood items brought in, is not more than 5kg per person.
For other food stuff allowed into Singapore, you may refer to the link: http://www.ava.gov.sg/InformationForTravellers/BringFood/index.htm.
－
