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[5.56]

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[john.41]

Mid 70's manufacture, nice condition,unknown barrel length, around $350.

[MCPO_SOCM_RET]

Shooters Bible and Blue Book are pretty similar. Note that these are not the current editions, but they're not too old either.

From what I can tell your 9 digit serial number starting with 37138, makes it a 1974 Model 37. (1974 = 371366001 - 371453500)

Unfortunately, in 1974, Ithaca tried a design change in the shell stop system, which proved to be faulty. They were reverted back to the original shell stops later that year. All these Model 37's had the serial number prefix of 381. Any of these that came to the factory for service were converted back to the original shell stops at no charge resulting in a serial number of 381000001 - 381030000. So, I'll take a WAG here and assume this particular Mod 37 wasn't sent back.

Looking at what I have, you are in the ballpark of (a properly maintained middle of the road normal wear and use value) $250-$300

Of course without knowing (in front of me) the overall condition you could be looking at more or less money. "Very Good/excellent" all original would bump you up to $350-$400 for example

Any gunsmith or reputable gun shop can do you an appraisal for a small nominal fee - and paperwork to back it up. Instead of just some guy on the internet said so and so.
I think I paid $20 for an appraisal last year. Might have been less, definitely wasn't more.