Can a police officer take your child?

In Washington - Yes, but only under certain conditions. For instance, police can take your child as result of a "probable cause" arrest, a court order, or via protective custody - typically relating to an immediate danger or threat to the child's safety.

Generally, children (under 18) are removed from their parent's care by Child Protective Services (CPS) after obtaining a court order. Police may assist CPS in that process but removal is conducted by CPS under authority of the court order.