The complicated arrangement by which some tax dollars are reinvested in downtown Fort Worth carries with it a requirement that somebody has to decide the best use of that money.That responsibility falls to the board members of the Downtown Tax Increment Financing District, and now they’re rethinking what has been a $3.4 million annual investment in free parking on nights and weekends.That’s a lot of money, but free parking is a key ingredient in downtown’s vibrant after-hours life. On many nights and most weekends, downtown streets, sidewalks, restaurants, shops and Sundance Square Plaza draw thousands of people — and hundreds of vehicles.Downtown in many cities doesn’t have that kind of vitality outside of the business day.But TIF board members also have to be good stewards of money entrusted to them. The city, county, hospital district, college district and Tarrant Regional Water District all let some of the additional tax money generated by downtown development since 1995 flow back to the TIF to be used in ways that boost even more economic activity.Inside the boundaries of Fort Worth, there are 11 tax increment financing districts similar to the one downtown, but the downtown TIF is by far the wealthiest.Between 1995 and 2012, downtown added $575 million in taxable property value, according to records on the city’s website.That means the TIF board has a lot of money to supervise. The $3.4 million for parking at six garages is a big part of it.“What is this money buying us versus what we could do in other arenas?” board member Charles Boswell asked at a meeting on Wednesday that was reported by Star-Telegram writer Sandra Baker.Last year, the board renegotiated a lease with Tarrant County on 250 parking spaces, dropping the payment to $25,000 annually from $400,000.The message is clear: The TIF intends to reduce parking costs. Still, board members know how important free night and weekend parking is to downtown.