Does new medical insurance coverage automatically become the primary coverage?

Answer

No, I'm checking on the CA State Law, but haven't found it yet. Here's the research I found so far.

From Blue Cross Administrators Manual

Medicare is the primary payor for employees age 65 or older in employer groups with less than 20 employees

When a group has fewer than 20 employees, Blue Cross is considered the secondary payor to Medicare and does not duplicate benefits that might be available under Medicare.

This is from Blue Cross of CA FAQ's

What is Coordination of Benefits (COB)?

A43.Coordination of Benefits (COB) is a provision to coordinate 100% of covered charges between multiple group health insurance and to designate the order in which the multiple carriers are to pay benefits. Under a COB provision, one Plan is determined to be primary and its benefits are applied to the claim. Part or all of the unpaid balance is usually paid by the secondary Plan to the limit of its liability. The coordination provisions apply separately to each member, per calendar year, and are largely determined by California law.

Answer

Here's the phamplet from Medicare http://www.medicare.gov/Publications/Pubs/pdf/02179.pdf

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