Arduino's analog input pulling down voltage when off
Atmega inputs only have high impedance when configured as such, and when the chip is powered on. When the chip is powered off (or underpowered), various things can happen. I'm with Nedd that the most probable cause is the protection diode, but it's not impossible that the pin gets reconfigured as output on power loss - if you're familiar with programming, you should know what "undefined behavior" is.

Making a separate voltage divider is by far the cheapest and easiest solution. That way, whatever effects may arise from the controller being powered down, they won't affect the rest of the system.