The New Haven PD told me that it's taking up to 6 months for some people. My LTCH expires in 6 months. I'm keeping my fingers crossed.
https://www.indianagunowners.com/forums/carry_issues_and_self_defense/6875-current_ltch_wait.html
ermahgerd... This thread already exists as a 210 page sticky.
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as long as you apply before your old lone expires, your application for your new ltch counts AS your ltch in the interim.