This paper presents a may-happen-in-parallel (MHP) analysis for OO languages based on concurrent objects. In this concurrency model, objects are the concurrency units such that, when a method is invoked on an object o2 from a task executing on object o1, statements of the current task in o1 may run in parallel with those of the (asynchronous) call on o2, and with those of transitively invoked methods. The goal of the MHP analysis is to identify pairs of statements in the program that may run in parallel in any execution. Our MHP analysis is formalized as a method-level (local) analysis whose information can be modularly composed to obtain application-level (global) information.