This video from the USA says about itself:
31 July 2016
Surprise! Two baby Gray Squirrels were delivered in the Screech Owl Nest Box yesterday. I took it down to clean and inspect it and it seem heavy – lo and behold mother squirrel was inside with two newly born helpless kittens not much bigger than large peanuts. Incredibly precious and the first time the owl nest box has been used in its location under the gable of the outbuilding.
Mother squirrel has to make a big jump to get to/from the nest box. My main concern is that that box is extremely hot in the morning with direct sun and just plain hot even in the shade in the afternoon. So far so good – but squirrels spend a very long time in the nest box as they are born so premature. Stay tuned!