Which thread handles the signal?

Read carefully signal(7) & pthread(7) & pthread_kill(3) & sigprocmask(2) & pthread_sigmask(3) -which you could use (to block SIGINT in unwanted threads). Read also a pthread tutorial.

Avoid using signals to communicate or synchronize between threads. Consider e.g. mutexes (pthread_mutex_lock etc...) and condition variables (pthread_cond_wait etc...).

If one of the threads runs an event loop (e.g. around poll(2)...) consider using signalfd(2).

If you send a signal to a process, which thread in the process will handle this signal is undetermined.

According to pthread(7):

POSIX.1 also requires that threads share a range of other attributes (i.e., these attributes are process-wide rather than per-thread):
...
- signal dispositions
...

POSIX.1 distinguishes the notions of signals that are directed to the process as a whole and signals that are directed to individual threads. According to POSIX.1, a process-directed signal (sent using kill(2), for example) should be handled by a single, arbitrarily selected thread within the process.

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If you want a dedicated thread in your process to handle some signals, here is an example from pthread_sigmask(3) shows you how to do it:

The program below blocks some signals in the main thread, and then creates a dedicated thread to fetch those signals via sigwait(3). The following shell session demonstrates its use:

$ ./a.out &
[1] 5423
$ kill -QUIT %1
Signal handling thread got signal 3
$ kill -USR1 %1
Signal handling thread got signal 10
$ kill -TERM %1
[1]+  Terminated              ./a.out

Program source

#include <pthread.h>
#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include <signal.h>
#include <errno.h>

/* Simple error handling functions */

#define handle_error_en(en, msg) \
        do { errno = en; perror(msg); exit(EXIT_FAILURE); } while (0)

static void *
sig_thread(void *arg)
{
    sigset_t *set = arg;
    int s, sig;

   for (;;) {
        s = sigwait(set, &sig);
        if (s != 0)
            handle_error_en(s, "sigwait");
        printf("Signal handling thread got signal %d\n", sig);
    }
}

int
main(int argc, char *argv[])
{
    pthread_t thread;
    sigset_t set;
    int s;

   /* Block SIGQUIT and SIGUSR1; other threads created by main()
       will inherit a copy of the signal mask. */

   sigemptyset(&set);
    sigaddset(&set, SIGQUIT);
    sigaddset(&set, SIGUSR1);
    s = pthread_sigmask(SIG_BLOCK, &set, NULL);
    if (s != 0)
        handle_error_en(s, "pthread_sigmask");

   s = pthread_create(&thread, NULL, &sig_thread, (void *) &set);
    if (s != 0)
        handle_error_en(s, "pthread_create");

   /* Main thread carries on to create other threads and/or do
       other work */

   pause();            /* Dummy pause so we can test program */
}