We develop a static cooperative game-theoretic framework for analyzing the impact of natural gas storage on interconnected gas and electricity markets. While increased utilization of gas storage has been proposed as a policy solution to fuel-security concerns in the electric power grid, the mode of interaction between gas storage units and electric power markets has not been investigated and some potential for cross-market manipulation exists. We investigate the potential for collusive behavior between gas storage units and power plants, whereby joint profits in the electricity and gas markets are increased by a strategy that involves the cooperative agents taking a loss in one market to the benefit of the other market. A cooperative strategy increases joint profits in scenarios when peak demand natural gas prices are high and the power plant(s) involved in the cooperative arrangement have relatively low marginal costs. The value of cooperation is not affected by whether gas storage units are physically connected to gas-fired power plants or if gas storage units inject gas into existing pipeline systems. While additional research into the nature of these competitive effects is needed, particularly in a repeated game context, our results point to the need to carefully consider the competitive effects of fuel security measures. A mechanism for monitoring of interactions between gas storage and power plants is likely warranted.