It's really hard to get something definitive on this - I have discovered that Ricinus communis wood, or a whole plant, is burned in the centre of a bonfire lit for religious reasons during a festival called Holika Dahan celebrated in India, without apparent ill effects, but that is burning outdoors, not indoors.
All other reliable information seems to pertain to the seeds or beans being highly toxic. Cornell University talks about aphids being killed within 24 hours of penetrating the phloem system of the plant, which suggests the sap itself is, to some extent toxic. On the other hand, the leaves from the plant are fed to silk worms, so either they're immune or the leaves don't contain toxic levels. Ricin is concentrated in the beans or seeds, and Wikipedia suggests that ricin is present in other parts of the plant, but in much smaller quantities. Even so, the oil from pressed castor beans is used in lamps in other parts of the world, mixed with kerosene usually. The fact its used in this way is probably meaningless, because once the beans are pressed, any ricin is left behind in the crushed beans, not actually in the oil's first pressing. I can find no warnings about wearing gloves when handling the plant, nor when pruning it.
There are various other sites which I don't consider trustworthy saying various things about Ricinus - everything from toxic pollen to toxic leaves and mass murder being possible by inhaling ricin (it's not), but finding out whether its completely safe to burn the wood appears to be next to impossible. If I find anything else that's definitive, I'll add it later.
UPDATE: Found another site (Mediterranean Garden Society) listing various plants which are dangerous if burned - Ricinus is not one of them - the one it mentions is Cestrum nocturnum, which produces toxic smoke if burned. It does include Ricinus as a toxic plant, but the entry is restricted to the seeds and their consumption/use. Residue from processing the beans for oil is 'cleaned' and turned into fertilizers, which might mean a possible allergic reaction if any dust is inhaled when the fertilizer is being distributed.