If all the segments are issued on the same ticket stock you will not be charged.
If it is two or three separate tickets in theory you will be.
In reality of course it is a different story.
Anyway you should just have to recheck after clearing customs in NYC you might not get charged if you have .../NYC/RNO on one ticket and RNO/DTW on an anotheri because once custom is cleared your bag will be checked all the way.
If you make a stopover of more than 24h in RNO you will get charge if just have a separate ticket to DTW