Better safe than sorry. Outside.
If I needed to keep it inside I would cut it into call blanks and marinate them in denatured alcohol for a few days. After that, putting them in a rolled up paper bag for a few days would slow down the evaporation of the alcohol and minimize cracking in the wood.
When I work with nasty looking spalted wood, sometimes I soak it in alcohol just so that I'm not filling my shop area with mold spores while I'm turning the piece.
