Technically weak research mostly supports the hypothesis, while strong research does not.

From The Impact of Gun Ownership Rates on Crime Rates: A Methodological Review of the Evidence by Gary Kleck. The research is not so much about answering the question "Does higher gun ownership lead to higher crime?" though it has a stab at that.

It must be tentatively concluded that higher gun ownership rates do not cause higher crime rates, including homicide rates.

No, I think the real question is "Why are there so many poorly designed research programs?" So much of what we know at the margin is founded on non-robust research findings. That is what Kleck is testing:

Purpose

This paper reviews 41 English-language studies that tested the hypothesis that higher gun prevalence levels cause higher crime rates, especially higher homicide rates.

Methods

Each study was assessed as to whether it solved or reduced each of three critical methodological problems: (1) whether a validated measure of gun prevalence was used, (2) whether the authors controlled for more than a handful of possible confounding variables, and (3) whether the researchers used suitable causal order procedures to deal with the possibility of crime rates affecting gun rates, instead of the reverse.

Results

It was found that most studies did not solve any of these problems, and that research that did a better job of addressing these problems was less likely to support the more-guns-cause-more crime hypothesis. Indeed, none of the studies that solved all three problems supported the hypothesis.

Conclusions

Technically weak research mostly supports the hypothesis, while strong research does not. It must be tentatively concluded that higher gun ownership rates do not cause higher crime rates, including homicide rates.