Subs can only take scalars as arguments; you can't pass a hash. You can pass a reference to the hash, though.

Also, you hold two references to the hash for no reason.

You want

HV* data_hash     = newHV();
SV* data_hash_ref = newRV_inc(data_hash);

...
call_perl_sub("test_callback", data_hash_ref);
...

SvREFCNT_dec(data_hash_ref);  /* Or motalise and return to caller */
SvREFCNT_dec(data_hash);
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Since we know data_hash_ref will outlive data_hash, we can avoid a ref count increment and decrement pair and simplify the above to the following:

HV* data_hash     = newHV();
SV* data_hash_ref = newRV_noinc(data_hash);

...
call_perl_sub("test_callback", data_hash_ref);
...

SvREFCNT_dec(data_hash_ref);  /* Or motalise and return to caller */
[download]