Why are there Closing Bids that are greater than or equal to Closing Asks in the CRSP Stock Database?

This situation would be known as crossed quotations. Basically crossed quotations happens when the Ask price of one Market Maker is the same or lower that the Bid price of another Market Maker. Though it is an unusual condition, it does occur in fast-moving markets. Exchanges have end-of-day cutoff filters in place for certain situations, but this crossed- quotations event is not filtered, as it is deemed acceptable by FINRA (Financial Industry Regulatory Authority) . Because these cases of conflicting bid and ask values legitimately exist,  CRSP also retains these quotes and makes them available in our database.