I did my own table to review pure numbers.
I took the top 11, and bottom 11 nations by "religiosity" and referenced numbers from Wikipedia's religious numbers and also added murder rates (most available crime data it seems) and then added in poverty
My own chart, once complete looked like this:
Country Religious Homicide Rate Religion Poverty
Azerbaijan 96.9 2.2 Muslim 11
Bangledesh 89.9 2.7 Muslim 26
Belarus 71.2 4.9 Christian 27.1
Democratic Republic Congo 95.8 30.8 Christian 71
Czech Republic 76.4 0.8 Unaffiliated 9
Denmark 83.5 0.9 Christian 13.4
Djibouti 96 3.4 Muslim 42
Egypt 94.9 1.2 Muslim 20
Estonia 59.6 5.2 Unaffiliated 17.5
France 63 1.1 Christian 6.2
Hong Kong 56.1 0.2 Unaffiliated NA
Indonesia 87.2 8.1 Muslim 13.33
Japan 57 0.3 Unaffiliated 16
Malawi 82.7 36 Christian 53
Mongolia 55.1 8.7 Buddhist 39.2
Morocco 99 1.4 Muslim 15
Norway 84 2.3 Christian NA
Senegal 96.4 8.7 Muslim 5.4
Sierra Leone 78 14.9 Muslim 70.2
Sri Lanka 69.3 3.6 Buddhist 8.9
Sweden 67 1 Christian NA
United Arab Emirates 79.6 0.8 Muslim 19.5
Note Religious in my graph is percentage of the population who are in the majority religion.
I then made this chart, sorted by highest homicide rate, and added in poverty for the sake of seeing other possible ideas / solutions:

Worth noting is the rate of each religion here too:
christian 7 31.82
muslim 9 40.91
buddhist 2 9.09
unaffiliated 4 18.18
In the top 5 most homicidal countries, Muslim is on the list twice.
In the top 11 (half), Muslim slots in 5 times, and 4 times in the bottom 11. This seems pretty even handed to me.
Although Buddhism has 100% of its representation in the top 11!
And finally, for the sake of mentioning it, unaffiliated is 75% in the least homicidal half of the chart.
My conclusion is that Islam does not lead to higher crime rates. At least not as the sole predictor. If there was a good predictor, from what I gathered above it is poverty. Most likely though, in my opinion the nations with the highest crime rates have a very complex explanation that includes poverty, diversity (or lack thereof), region and religion.