you are mixing DAO with ADO, just stick with DAO in an Access environment, modified code with corrections below. backup your db first!!

Sub ExportTstar()
    '-----------------------------------------------------------------
    'FT: comment out below
    'Dim cnn As New DAO.Connection
    '-----------------------------------------------------------------
   
    Dim db As DAO.Database
    Dim rs As DAO.Recordset 'remove "NEW"
    Dim fso As Object
    Dim ts As Object
    Dim Abbrev As String
       
        Abbrev = InputBox("Please enter Enity")
    If Abbrev = "" Then
        MsgBox "Abort", vbCritical
        Exit Sub
    End If
    '-----------------------------------------------------------------
    'FT: create db object
    Set db = CurrentDb
    '-----------------------------------------------------------------  
 
    Set fso = CreateObject("Scripting.FileSystemObject")
    Set ts = fso.CreateTextFile("c:\" & Abbrev & ".ctf", True)        

    '-----------------------------------------------------------------
    'FT: comment out
    'Set rs = db.OpenRecordset("APR_DRG")
    'Set cnn = CurrentProject.Connection  
    '-----------------------------------------------------------------
    'FT: is entity a numeric field? if so then (commented out below)
    'Set rs = db.OpenRecordset("SELECT * FROM [APR_DRG] WHERE [Entity]= " & Abbrev)
   
    'FT: is entity a text field? if so then
    Set rs = db.OpenRecordset("SELECT * FROM [APR_DRG] WHERE [Entity]= '" & Abbrev & "'")
    If rs.RecordCount = 0 Then
        MsgBox "record does not exist!!", vbExclamation
        Set db = Nothing
        Exit Sub
    End If
    '-----------------------------------------------------------------
   
    With rs
        '-----------------------------------------------------------------
        'FT: comment out
        'Set .ActiveConnection = cnn
        '-----------------------------------------------------------------
        .MoveFirst
        Do While Not .EOF
            ts.WriteLine "CHA," & ![ACCOUNT_NO] & ", " & ![Discharge_Date]
            ts.WriteLine ".APRDRG :" & ![APR20_DRG]
            ts.WriteLine ".APR_MDC" & ![APR_MDC]
            ts.WriteLine ".APRSUB :" & ![APR20_SOI]
            ts.WriteLine ".APRRMOR :" & ![APR20_ROM]
            ts.WriteLine "APR_CMI :" & ![APR20_CMI]
            ts.WriteLine "3MDRG_V24 :" & ![CMS24_DRG]
            ts.WriteLine "3MDRG_V25 :" & ![CMS25_DRG]
                       
        .MoveNext
        Loop
    End With
   
    Set rs = Nothing
    'Set cnn = Nothing
    ts.Close
    Set ts = Nothing
    Set fso = Nothing
    MsgBox "Done"

End Sub