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Interesting question, I never though about if there is any way to test a black holes charge. My guess is that we only can assume if it is there based on the theory right now
found a relevant answer at http://www.astro.umd.edu/~miller/teaching/questions/blackholes.html "black holes can have a charge if they eat up too many protons and not enough electrons (or vice versa). But in practice this is very unusual, since these charges tend to be so evenly balanced in the universe. And then even if the black hole somehow picked up a charge, it would soon be neutralized by producing a strong electric field in the surrounding space and sucking up any nearby charges to compensate. These charged black holes are called "Reissner-Nordstrom black holes" or "Kerr-Newman black holes" if they also happen to be spinning." -Jeremy Schnittman
Calculate the black hole's mass. Put a charged particle somewhere in the vicinity of the black hole. Measure acceleration. Do math.
That much is obvious given an assumption that charged fields work proberly through a blackhole, which was not obvious particularily given aljandro's statement. After confirming that the charge of a blackhole can interact with being impeded by the singularity, there are a lot of obvious ways to check the charge
Will that work? Or to put it particle-ish-ly, how is the information about a charge inside an event horizon able to escape?