What (if any) is the leakage current through a NPN (C-E)?
Let's have a look at the datasheet:



At room temperature the maximum leakage is 15nA at 30V, implying a 150mV voltage. It will be less at 3V, but not necessarily proportionally less. The maximum leakage at a Tj of 150°C is 5uA which would be excessive. So, how much of that is because they don't want to make time consuming low-current tests on an inexpensive part? Here's a typical curve from a similar part (2N4401) which shows you might typically run into trouble around 100°C Tj (50nA). 



It's usually considered bad engineering to depend on typical values (though you see it done with careful forethought all the time in many commercial products), but I have to conclude that it is unlikely (approximately zero percent likelihood) that ICBO leakage is causing the problems in your setup. 

Note that this is the leakage with Vbe ~=0. If you leave the base open or (worse) have it connected to something that acts as an antenna, all bets are off. As Dave Tweed points out the gain of the transistor can amplify the current if you leave the base open. It could conceivably have a gain of 100 at 1nA Ib.  So, don't do that! Make sure there is a resistance from base to emitter when you want the transistor 'off'. Even 1M from base to emitter is enough to make that problem go away- more likely you're driving it from a push-pull output and it will have a very low resistance to keep the ICBO current from being amplified.