Is there any Corelation between the SHA256 and SHA512 hash of the same data? Is there any Corelation between the SHA256 and SHA512 hash of the same data ?
No.

Knowing $h = \operatorname{SHA-256}(m)$ without $m$ doesn't help you to find $h' = \operatorname{SHA-512}(m)$, or vice versa, except insofar as you can use $h$ to test a guess $m^*$ for what $m$ might be, by checking $$h \stackrel?= \operatorname{SHA-256}(m^*).$$

The same goes for all of the SHA-2 functions {SHA-224, SHA-256, SHA-384, SHA-512, SHA-512/224, SHA-512/256}.  It also goes for the fixed-length SHA-3 functions {SHA3-224, SHA3-256, SHA3-384, SHA3-512}.

Note: The extendable-output SHA-3 functions SHAKE128 and SHAKE256 have the property that SHAKE128-$n$ and SHAKE128-$m$ share a common prefix—in other words, SHAKE128 and SHAKE256 produce infinite-length outputs for any input and you just use a finite prefix of the length you requested.  However, they are otherwise independent of the SHA-2 and fixed-length SHA-3 functions, and of the related SHA-3 constructions KMAC, TupleHash, and ParallelHash.

You can make your own family of independent functions in the privacy of your own living room by picking a fixed-length prefix $p$ in some set like {foo, bar, baz, qux, zot} and using, say, $m \mapsto \operatorname{SHAKE128}(p \mathbin\| m)$ or $m \mapsto \operatorname{SHA-512/256}(p \mathbin\| m)$; for each distinct $p$, this can be modeled as an independent uniform random function as in a random oracle, as long as you always use a prefix.*†



* Note that if you use $H_p\colon m \mapsto \operatorname{SHA-256}(p \mathbin\| m)$, you have the property that knowledge of $H_p(m)$ lets you compute $H_p(\operatorname{pad}(m) \mathbin\| m')$ for any suffix $m'$, which is quite improbable for a uniform random function.  This is called a length extension attack.  The SHA-3 functions dispense with this property, as do SHA-512/224 and SHA-512/256.

† Actually the set of prefixes need not be fixed-length—it is sufficient that it be prefix-free, meaning that if $p \ne p'$ are in the set of possible prefixes, then neither one is a prefix of the other.  For instance, length-encoded tags like 3 foo, 4 quux, 11 hello world would work too, as long as the length is encoded uniquely.