Thread safety of a static random number generator

I have a bunch of threads, each one needs a thread safe random number. Since in my real program threads are spawned and joined repeatedly, I wouldn't like to create random_device and mt19937 each time I enter a new parallel region which calls the same function, so I put them as static:

#include <iostream>
#include <random>
#include <omp.h>

void test(void) {
    static std::random_device rd;
    static std::mt19937 rng(rd());
    static std::uniform_int_distribution<int> uni(1, 1000);

    int x = uni(rng);
#   pragma omp critical
    std::cout << "thread " << omp_get_thread_num() << " | x = " << x << std::endl;
}

int main() {
#   pragma omp parallel num_threads(4)
    test();
}

I cannot place them as threadprivate because of Error C3057: dynamic initialization of 'threadprivate' symbols is not currently supported. Some sources say random_device and mt19937 are thread safe, but I haven't managed to find any docs which would prove it.

1. Is this randomization thread safe?
2. If no, which of the static objects can be left as static to preserve thread safety?