using Switch like logic in T-SQL

You need to use If/Else If structure, like this:

If @Type = 1
    Begin
        INSERT INTO dbo.Credit (
                CompanyName,
                PhoneNumber,
                City,
                State
        ) VALUES ( 
                @CompanyName,
                @PhoneNumber,
                @City,
                @State) 
    End
Else If @Type = 2
    Begin
        INSERT INTO dbo.Debit (
                CompanyName,
                PhoneNumber,
                City,
                State
        ) VALUES ( 
                @CompanyName,
                @PhoneNumber,
                @City,
                @State) 
    End
Else If @Type = 3
    Begin
        --ETC
    END