My 2003 Honda CR-V had been showing a Maint Req light on the dash. After having diagnostics run, a diagnostic code of P1456 with a message of No DTC Definition Found. Also showed was the code P0845 Transmission Fluid Pressure Sensor/Switch B Circuit. What do those two mean?

P1456--EVAP Emission Control System Leak Detected (Fuel Tank System). Try tightening the gas cap 3 clicks. If the code returns, after being cleared with a code reader, replace the gas cap. The CEL will go out on its own, if the cap was not on tight enough.

P0845--Third gear pressure switch. Check connector and wiring--if code persists, try replacing the switch.

Be sure to change the ATF every 30,000 miles or 2 years, whichever comes first:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-selected-other-vehicles-46563-14.html#post2634481

Sludging can affect pressure to the switch.

Thanks, the check engine light has turned on before when I have forgotten to tighten the gas cap all the way, but this time that light isn't on. I'm wondering why the maintenance required light would go on? Could that be because of the transmission fluid?

See if this fits:

Topping off the gas tank can easily damage the EVAP Emission Control System on modern day vehicles. They are made to handle fumes, not gasoline. If you've been doing this, repairs can be expensive ($400+).