This paper deals with a two-person zero-sum search game called {\it search allocation game} (SAG) with a searcher
and a target as players, taking account of false contacts.
The searcher distributes his searching resource in a search space to detect the target and the target moves to evade the searcher.
The searcher obtains a profit of target value on detection of target but expends cost for the search.
The payoff of the game is the expected reward defined by obtained target value minus expended searching cost.
The searcher's strategy is denoted by a distribution plan about where and when he distributes his searching resource
and the target strategy is the selection of a path to follow from some options.
In the search operation, any sensor cannot get rid of false contacts caused by signal processing noises
and real objects similar to the true target under noisy environment.
On their happening, they make the searcher waste some time for investigation and interrupt the search operation for a while.
There have been few researches dealing with the SAG with the false contacts. In this paper,
we model the game with false contacts by a stochastic process and discuss a general procedure to
derive an equilibrium point through a nonlinear programming method for a searcher's best response to the target's behavior.