Is the error message valid?
Error on crc32_append

It's better to use CSP_ERR_NONE.

Is the error message unnecessary?
There is also a similar error message-less function called zasert_equal().

Add the error message to all assert function.

Isn't the purpose of this test to check that an error occurs if csp_crc32_append() is not called ?
If the purpose is to create “if length < sizeof(crc)”, the test below can be read as working

memcpy(packet->data, "Hello", 5);
packet->length = 5;

ret = csp_crc32_verify(packet);

rename function name to test_crc_verify_without_crc

Please update also comment.

/* check error if length < sizeof(crc) */

Please format the code by zephry's clang-format.
Maybe you need to fix the below.

diff --git a/src/crc32.c b/src/crc32.c
index c206407..ec41a62 100644
--- a/src/crc32.c
+++ b/src/crc32.c
@@ -40,7 +40,7 @@ static void after(void *data)
 ZTEST_F(crc, test_crc_verify_without_crc)
 {
        csp_packet_t *packet = fixture->buf;
-       packet->length = sizeof(uint32_t)-1;
+       packet->length = sizeof(uint32_t) - 1;
        int ret;
 
        /* check error if length < sizeof(crc) */
@@ -72,8 +72,8 @@ ZTEST_F(crc, test_crc_with_header)
        packet->length = 5;
 
        /* Check with header.
-       * This simulate CSP_21 define on csp_crc32_append().
-       */
+        * This simulate CSP_21 define on csp_crc32_append().
+        */
        csp_id_prepend(packet);
        crc = csp_crc32_memory(packet->frame_begin, packet->frame_length);
        /* Convert to network byte order */

Why set the sizeof(uint32_t) - 1 ?
I think this setting is inconsistent with the test name without crc.

I was trying to test here : https://github.com/libcsp/libcsp/blob/develop/src/csp_crc32.c#L116-L118
But now I see that I'm not trying any more to test here : https://github.com/libcsp/libcsp/blob/develop/src/csp_crc32.c#L132-L134
Should I test the first error with the size part ? If not I will just go back to the previous code.

I understand your purpose, but I think:

If you set the sizeof(uint32_t) - 1, you need to set the 3 byte data to packet->data.
Certainly, there is no point in setting data since it will be rejected by the length check, but I think the test code should comply with the original usage as much as possible.

And, one more things.

If we executes csp_crc32_verify() without csp_crc32_append(), as you say, there are two error routes.

1. packet length less than 4 byte ( https://github.com/libcsp/libcsp/blob/develop/src/csp_crc32.c#L116-L118 )
2. CRC value is unmatched ( https://github.com/libcsp/libcsp/blob/develop/src/csp_crc32.c#L132-L134 )

So in this test, we should be test the both case like below.
(It's just in example)

    csp_packet_t *packet = fixture->buf;
    packet->length = 0;

    ret = csp_crc32_verify(packet);
    zassert_equal(ret, CSP_ERR_CRC32, "Error on csp_crc32_verify");

    memcpy(packet->data, "Hello", 5);
    packet->length = 5;
    ret = csp_crc32_verify(packet);
    zassert_equal(ret, CSP_ERR_CRC32, "Error on csp_crc32_verify");

Anyway let's discuss later in F2F.

Please add the causes to the content of the error messages so that it's clear which error is occured.

same as line 48.