Causation - no, correlation - very likely. Policies and politicians that cause strict gun laws also cause higher crime, and conversely, politicians, when faced with higher crime, would reflectively reach for the only leverage they have - stricter laws. Which would usually be futile (at least without many other measures, which aren't used that frequently). Thus, in practice, strict gun laws and crime - at least in the US - often go together. There are exceptions of course - very safe places could introduce strict gun laws out of virtue signaling, moral panic or other considerations. But the common case is as per above.
