Is there a building code for shower tile? (CA)
There is no code requirement/ restriction for installing tile over tile... for showers or otherwise. 

However, there are many trade organizations in the construction industry that investigate, test, etc. products (i.e.: roofing, concrete, tile, paint, etc.) so that various materials are installed in the proper (most durable long-lasting) manner. 

For tile, we follow the Tile Council of North America (TCNA).  They recommend various methods of installation for countertops, showers, retrofits, etc.  

Check here: http://www.tcnatile.com/

I’d also verify recommended method of installation by the tile company of the actual tile you select. 

I’m guessing they’d recommend you remove the old tile for lots of reasons, (i.e.: loose tile, bad grout, mold, lack of adhesion, incompatible tile, etc., but check out their recommendation.