How does karmic law explain when a child by birth sick or retard ? Does it mean that karma's of both parents, brothers and sisters and person himself have done some bad karma's in their previous life hence they are brought up to this state in their present life.
It is mostly the karma of the individual, but yes others can be involved. There is never, (in Hinduism, anyway) the concept of 'no fault', Karma can be quite complex and intertwined, and the idea is to accept it with as much cheerful diligence as possible, else it just continues. That's why revenge is so low-minded as well. I realise this is hard to explain, and even harder to understand unless you think dharmicly.
We just view karma like gravity ... a natural law. But it is complicated when viewed through a 'thinking ' lens.