The 2nd Michigan was part of a Reconaissance in Force and suffered only 1 person Wounded in Action.

From http://www.fullbooks.com/The-Great-Conspiracy-Part-3-2.html

"Richardson orders up the 12th New York, Colonel Walrath, to the left of our battery. Forming it into line-of-battle, Richardson orders it to charge through the woods upon the Enemy. Gallantly the regiment moves forward, after the skirmishers, into the woods, but, being met by a very heavy fire of musketry and artillery along the whole line of the Enemy's position, is, for the most part, thrown back in confusion--a mere fragment* remaining in line, and retreating,--while the howitzers, and Cavalry also, are withdrawn.

Meantime, however, Richardson has ordered up, and placed in line-of-battle, on the right of our battery, the 1st Massachusetts, the 2d Michigan (his own), and the 3d Michigan. The skirmishers in the woods still bravely hold their ground, undercover, and these three regiments are plucky, and anxious to assault the Enemy. Richardson proposes to lead them in a charge upon the Enemy's position, and drive him out of it; but Tyler declines to give permission, on the ground that this being "merely a reconnaissance," the object of which--ascertaining the strength and position of the Enemy--having been attained, a further attack is unnecessary. He therefore orders Richardson to "fall back in good order to our batteries on the hill,"--which he does.

Upon reaching these batteries, Richardson forms his 2d Michigan, in "close column by division," on their right, and the 1st Massachusetts and 3d Michigan, in "line of battle," on their left--the 12th New York re-forming, under cover of the woods at the rear, later on. Then, with our skirmishers thrown into the woods in front, their scattering fire, and the musketry responses of the Rebels, are drowned in the volume of sound produced by the deafening contest which ensues between our Artillery, and that of the Enemy from his batteries behind Bull Run.

This artillery-duel continues about one hour; and then seems to cease by mutual consent, about dusk--after 415 shots have been fired on the Union side, and have been responded to by an equal number from the Rebel batteries, "gun for gun"--the total loss in the engagement, on the Union side, being 83, to a total loss among the Enemy, of Thursday night, Richardson retires his brigade upon Centreville, in order to secure rations and water for his hungry and thirsty troops,--as no water has yet been found in the vicinity of the Union batteries aforesaid. On the morrow, however, when his brigade re-occupies that position, water is found in abundance, by digging for it.

This premature attack, at Blackburn's Ford, by Tyler, against orders, having failed, throws a wet blanket upon the martial spirit of McDowell's Army. In like degree is the morale of the Rebel Army increased.

It is true that Longstreet, in command of the Rebel troops at Blackburn's Ford, has not had things all his own way; that some of his artillery had to be "withdrawn;" that, as he acknowledges in his report, his brigade of three Virginia regiments (the 1st, 11th, and 17th) had "with some difficulty repelled" the Union assault upon his position; that he had to call upon General Early for re-enforcements; that Early re-enforced him with two Infantry regiments (the 7th Louisiana and 7th Virginia) at first; that one of these (the 7th Virginia) was "thrown into confusion;" that Early then brought up his own regiment (the 24th Virginia) under Lieutenant Colonel Hairston, and the entire seven guns of the "Washington Artillery;" and that but for the active "personal exertions" of Longstreet, in "encouraging the men under his command," and the great numerical superiority of the Rebels, there might have been no Union "repulse" at all. Yet still the attack has failed, and that failure, while it dispirits the Patriot Army, inspires the Rebel Army with renewed courage.