Even if neither stdin nor stdout are ttys we may still have /dev/tty

available to us.

check.c

@@ -109,9 +109,9 @@ check_user(validated, interactive)
 	    if (user_askpass == NULL)
 		log_error(NO_MAIL,
 		    "no askpass program specified, try setting SUDO_ASKPASS");
-	} else {
+	} else if (!ISSET(tgetpass_flags, TGP_STDIN)) {
 	    /* If no tty but DISPLAY is set, use askpass if we have it. */
-	    if (!user_ttypath && !ISSET(tgetpass_flags, TGP_STDIN)) {
+	    if (!user_ttypath && !tty_present()) {
 		if (user_askpass && user_display && *user_display != '\0') {
 		    SET(tgetpass_flags, TGP_ASKPASS);
 		} else if (!def_visiblepw) {

sudo.h

@@ -240,6 +240,7 @@ int mkstemp		__P((char *));
 char *sudo_goodpath	__P((const char *, struct stat *));
 char *tgetpass		__P((const char *, int, int));
 int find_path		__P((char *, char **, struct stat *, char *));
+int tty_present		__P((void));
 void check_user		__P((int, int));
 void verify_user	__P((struct passwd *, char *));
 #ifdef HAVE_LDAP

tgetpass.c

@@ -309,3 +309,13 @@ handler(s)
     if (s != SIGALRM)
 	signo = s;
 }
+
+int
+tty_present()
+{
+    int fd;
+
+    if ((fd = open(_PATH_TTY, O_RDWR|O_NOCTTY)) != -1)
+	close(fd);
+    return(fd != -1);
+}