An infant boy was given up at a hospital in New London under the state’s ‘‘safe haven’’ law, which protects parents from being prosecuted for abandonment. The Department of Children and Families said 20 infants have been taken to hospitals under the law since it took effect in 2000. The boy taken to Lawrence and Memorial Hospital in New London last week is currently staying in a foster home and will be put up for adoption. DCF Commissioner Joette Katz said ‘‘safe haven’’ babies typically generate significant adoption interest. Under the law, infants less than a month old can be left at any hospital emergency department and DCF will assume custody.