If the limbs are brown and dry (brittle) then you can cut the limbs off as they won't return. If however the limbs are still supple but just the needles are dead then leave then and wait to see what happens. They may return.
I am not able to tell from the description why they are turning brown. It may be due to a fungal disease of the needles or branches. These are usually not too severe but at times may require spraying when conditions favor disease development. Your County Extension Office can suggest an appropriate spray product. I suggest starting with just pruning out and discarding the dead limbs and seeing if that takes care of the problem.
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