That is certainly an interesting question!
First, to clarify definitions:
To be considered venomous the toxic substance must be produced in specialized glands or tissue. Often these are associated with some delivery apparatus (fangs, stinger, etc.), but not necessarily.
To be poisonous, the toxins must be produced in non-specialized tissues and are only toxic after ingestion.
Interestingly, many venoms are not poisonous if ingested.
I know of at least three species that produce both poison and venom. One is a snake (although not a rattlesnake, which are, in fact, edible): Rhabdophis tigrinus, which accumulates toxins in its tissues, but also delivers venom via fangs. The other two are frogs: Corythomantis greeningi and Aparasphenodon brunoi, which have spines on their snout that they use to deliver the venom.
 Meier and White (eds.). 1995. Handbook of clinical toxicology of animal venoms and poisons. Boca Raton, Fla.: CRC Press, 477p.
 Hutchinson et al. 2007. Dietary sequestration of defensive steroids in nuchal glands of the Asian snake Rhabdophis tigrinus. PNAS 104(7): 2265-2270.
 Jared et al. 2015. Venomous frogs use heads as weapons. Current Biology 25, 2166-2170.