Is local static variable initialization AS Safe in signal handler (Async Signal Safe)?

Question

I wonder which I can use in my signal handler?

void my_signal_handler(int signo, siginfo_t* info, void* arg) {
    static std::atomic_flag my_flag = ATOMIC_FLAG_INIT;
    if (my_flag.test_and_set()) {
       ...
    } else {
       ...
    }
    ...
}

OR use std::atomic_flag as global static variable:

static std::atomic_flag my_flag = ATOMIC_FLAG_INIT;

void my_signal_handler(int signo, siginfo_t* info, void* arg) {    
    if (my_flag.test_and_set()) {
       ...
    } else {
       ...
    }
    ...
}

According to When do function-level static variables get allocated/initialized?

local static variable is initialized first time the function is hit, but if the containing function is a signal handler, the question here is if the initialization of local static varible is Async Signal Safe or not? Because MT Safe is not enough in signal handler environment.

Please anyone can clarify about this, thanks in advance.