Thread: global variable at dynamic library

Hello! I have a couple of functions that MUST share a single variable. These functions will be compiled into a dynamic library (.so) and this library will be accessed by multiple threads. Is this method thread-safe, or I must use mutexes to prevent corruption of the global variable?

Code:

// foo.h
void foo1();
void foo2();

Code:

// foo.cpp
static int foo_flag = 0;
void foo1() {
    // uses foo_flag
}

void foo2() {
    // uses foo_flag
}

Thanks any help!