It's (probably) not a part of the TTX software....never heard of it being part of TTX in the last 25 years.
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But:
WY DOR FAQs:
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Use tax Form 44:
44-ConsumersNon-LicensedVendors.pdf - Google Drive
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Instructions for Form 44:
I asked to local tax prep professionals and one said they never heard of the Form 44, and the other said there is no way to file it. So who knows?
Opinion: I suspect because WY may not have a way to rigorously enforce it. They might have staff who primarily go after someone buying large amounts of untaxed stuff from out of state. Ask your local state representative about it.
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We only know what we read in their Use/Sales tax FAQs.
Certainly, the form 44 instructions link I posted above, does show an address to mail the form and your payments to.
The instructions do seem somewhat outdated, describing examples for dates in 2009 and 2010, but the instructions themselves are dated Jan of 2020, so it's likely still in effect. A Google search doesn't show any hits (in the first couple pages of hits) to that indicate it's been suspended.