The simplest hypothesis of DNA strand symmetry states that proportions of nucleotides of the same base pair are approximately equal within single DNA strands. Results of extensive empirical studies using asymmetry measures and various visualization tools show that for long DNA sequences (approximate) strand symmetry generally holds with rather rare exceptions. In the paper, a formal definition of DNA strand local symmetry is presented, characterized in terms of generalized logits and tested for the longest non-coding sequences of bacterial genomes. Validity of a special regression-type probabilistic structure of the data is supposed. This structure is compatible with probability distribution of random nucleotide sequences at a steady state of a context-dependent reversible Markov evolutionary process. The null hypothesis of strand local symmetry is rejected in majority of bacterial genomes suggesting that even neutral mutations are skewed with respect to leading and lagging strands.