Deflections of jets discharged into a reservoir with a free surface are investigated numerically. The jets are known to deflect towards either side of the free surface or the bottom, whose direction is not determined uniquely in some experimental conditions, i.e. there are multiple stable states realizable in the same condition. The origin of the multiple stable states is explored by utilizing homotopy transformations in which the top boundary of the reservoir is transformed from a rigid to a free boundary and also the location of the outlet throat is continuously moved from mid-height to the top. We depicted bifurcation diagrams of the flow compiling the data of numerical simulations, from which we identified the origin as an imperfect pitchfork bifurcation, and obtained an insight into the mechanism for the direction to be determined. The parameter region where such multiple stable states are possible is also delimited.