We focus on the aggregation of citizen preferences for public projects through civic crowdfunding. Existing civic crowdfunding mechanisms consider only agents with positive valuation towards the public project. Moreover, these mechanisms assume that each agent has a symmetric belief about the project getting provisioned. As public projects aim to cater to the majority, they should be provisioned only if the majority prefers it. To incorporate negative valuations, we propose a methodology to convert existing civic crowdfunding mechanisms for positive preferences to cater to markets having both types of agents. Specifically, we adapt existing PPR and PPS mechanisms to design PPRN and PPSN, that incentivize agents to contribute towards or against the project’s provision: based on their preference. Besides, to address asymmetric beliefs, we propose a novel reward scheme, Belief Based Reward (BBR) based on Robust Bayesian Truth Serum (RBTS) mechanism. BBR rewards agents based on their belief towards the project’s provision. Using this reward scheme, we introduce a general mechanism for civic crowdfunding which allows for agents having asymmetric beliefs towards the project getting provisioned and incentivizes them to contribute towards the project’s provision. We illustrate the general mechanism by designing two novel mechanisms, namely PPRx and PPSx, adapting PPR and PPS respectively, and prove that in both the mechanisms the project is provisioned at equilibrium.