How can I check if char* variable points to empty string?

Check if the first character is '\0'. You should also probably check if your pointer is NULL.

char *c = "";
if ((c != NULL) && (c[0] == '\0')) {
   printf("c is empty\n");
}

You could put both of those checks in a function to make it convenient and easy to reuse.

Edit: In the if statement can be read like this, "If c is not zero and the first character of character array 'c' is not '\0' or zero, then...".

The && simply combines the two conditions. It is basically like saying this:

if (c != NULL) { /* AND (or &&) */
    if (c[0] == '\0') {
        printf("c is empty\n");
    }
}

You may want to get a good C programming book if that is not clear to you. I could recommend a book called "The C Programming Language".

The shortest version equivalent to the above would be:

if (c && !c[0]) {
  printf("c is empty\n");
}

My preferred method:

if (*ptr == 0) // empty string

Probably more common:

if (strlen(ptr) == 0) // empty string