Do I need CYA on an indoor pool ?

You should. You may only need about 20 ppm worth since you're obviously not worried about the sun, but the CYA helps to buffer the effects of unprotected chlorine against the skin and surfaces. Chlorine with no CYA at all is exponentially strong.
 
Chlorine in a pool without CYA can be harsh.

20 ppm or so of CYA buffers the chlorine. To learn how it works read about available chlorine and reserve chlorine when you have CYA in CYA - Further Reading
 
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