tl;dr Crime doesn't have one trend, it has multiple fascinating trends. The one pretty uniform trend is 1945 saw a crime boom.

1,565,541 major crimes were reported in 1945 compared to 1,517,026 & 1,531,272 in 1940 and 1941.

A potential problem with your question is that crime wasn't in a steady state before the war. If you look at e.g. the homicide rate you'll see a long term decline in the homicide rate with a 1944-1946 boom that only extends as far as to negate all the post 1940 gains in reducing the homicide rate. To throw in another homicide stat: Murder in 1944 was 7.5% below the 3 year pre-war average. I'm not going to do a lot with this caveat in the rest of the piece but it should be mentioned.

Rape and aggrevated assault grew continuously during the war with the exception of 1945 property crime was lower than the 1937-1939 average.

source: http://www.icpsr.umich.edu/icpsrweb/NACJD/studies/3666 .

page 125 of DS3: Uniform Crime Reports, 1944-1959 has a fantastic graph "% Change in crime since 1939" which includes the entire war. and page 453 has a great table (for cities over 25k) which has the raw numbers for major crimes.

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an excerpt

The long-term-crime-trend information [graph from 1940-1952]...point up an almost uninterrupted rise over the years in crimes of rape and other feloneous assaults to very high points in 1952. Murder and negligent manslaughter have followed generally similar trends, declining during the early war years, up in 1945 and 1946 then declining again until 1959. [larceny and burglary] decline during the early parts of WW2 but increased rather steadily since.

while Auto Theft would decline in the immediate post war years, this specific crime exploded during the period of US involvement in WW2.