Looking at https://en.wikipedia.org/wiki/Political_party_strength_in_New_Hampshire for a quick rundown of party control over time, no, this looks like this is literally the closest the chamber has ever been to parity. If you mean 'close seats flipping in recounts,' then yes, with so many seats and so relatively few votes for each seat, I expect it has. There's also the notable case of Durkin v Wyman for the 1974 Senate seat, which ultimately was declared by the US Senate to be vacant and a new election held because the deadlocked Senate couldn't come to an agreement on the resolution otherwise (https://www.senate.gov/about/origins-foundations/electing-appointing-senators/contested-senate-elections/137Durkin_Wyman.htm).