Signals over millimeter wave (mmWave) bands suffer from severe path loss and are easily blocked by obstacles, which greatly degrades the link quality and reliability of mmWave communications. One of the promising ways to overcome this challenge is multi-connectivity, which enables a user to associate with multiple small cells simultaneously. In this paper, we investigate the association problem of a given user to multiple mmWave base stations (mBSs), which we termed user-centric association. In particular, we consider an intelligent reflecting surface (IRS)-aided ultra-dense mmWave communication system, in which multiple distributed IRSs are deployed to expand the coverage of mmWave signals to blind spots. The user-centric association problem is formulated to maximize the user achievable sum-rate with respect to the mBS-user association, auxiliary IRS selection, and power allocation in a combinatorial manner. The original optimization problem is a mixed-integer nonlinear programming problem, which is NP-hard. To solve it, we first relax the formulated problem into a continuous one, then decouple it into three subproblems by utilizing decomposition technique, and finally propose an alternating iteration based algorithm to obtain the optimal solution. Numerical simulations show that the user sum-rate can be greatly improved by the joint optimization scheme.