In the United States (U.S), cannabis policies have been increasingly liberalized whereas tobacco policies have been increasingly stringent. Given the high prevalence of cannabis and tobacco dual use, there are concerns that a policy regulating one substance may unintendedly influence the other. This study examined the responsiveness of the demand for cannabis joints and cigarettes when price varied. The study included 338 adult participants (21+) who used both cannabis and tobacco and lived in one of the U.S. states with recreational cannabis legalized by the time of interview in 2019. They completed hypothetical purchase tasks to indicate the quantity desired of cannabis joints and cigarette packs 1) when only one substance was available with escalating prices and 2) when both substances were concurrently available with escalating prices of cannabis joints and a fixed price of cigarette packs. We estimated 1) the own-price elasticity of demand for each substance using nonlinear exponential demand model, and 2) the cross-price elasticity of demand at aggregate level using nonlinear exponential demand model and at individual level using log-linear demand model. The estimates for the rate of change of own-price elasticity (α) were 0.0011 (SE=0.000039, p<0.001) for cannabis joints and 0.00095 (SE=0.000037, p<0.001) for cigarette packs. The aggregate-level estimates of cross-price elasticity (I=13.032, SE=0.34, p<0.001; β=0.0029, SE=0.0021, p>0.05) suggest an independent relationship between the two substances. At individual level, 78.70% of the participants treated the two substances as independent, 17.46% as complements, and 3.85% as substitutes. For most adults who used both cannabis and tobacco in the U.S., cannabis joints and cigarettes had an independent relationship. Policies regulating the price of cannabis may not have large unintended consequences on cigarette use.