The bill cleared a House panel Wednesday as Republicans scrutinized the estimates.
The analysis says parents and caretakers of children 6 years or older would be affected.
The $18.7 million net cost notably includes $22.3 million more in anticipated case management state costs and $3.7 million in estimated state savings from disenrollments, assuming a 2020 program start.
The analysis assumes another $15.3 million in federal costs.
The bill by Republican House Speaker Beth Harwell seeks a waiver under President Donald Trump's administration, which is allowing state Medicaid work requirements.
TennCare's Ashley Reed says the department's stance on the bill is "deferred."
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