In a word, yes.  If it is a non-bolt action single shot and shoots plain base lead bullets (or in this case, .22 rf) it is legal.  Merry Christmas!

Froggie

Section 1.0   Single Shot Rifle

 

A single shot rifle is defined as a breech loading cartridge rifle without magazine or provision for additional cartridges, in which the action must be operated, and in which a cartridge or shell must be manually inserted for each shot. Bolt action rifles are specifically excluded regardless of age or model. The action may be of the falling block, tipping block, rolling block, tip up or any similar type whether made recently or in years past. Regardless of the action type, the rifle shall basically conform to the style and appearance of rifles made from the Civil War era to 1914 period either here in the U.S. or elsewhere. This will include both factory made rifles and rifles fabricated by custom gun makers of that period.

The 22 matches are run under the same rules as any other ASSRA match held at Beeson range.

Did you check the source I listed.  It goes into more detail.

Looking along the line at EG for the 22-only shoots the various 22 rf martinis probably have the strongest showing of all the various single shots that have been done in 22 rf. 
 Unless they have been well and truly buggered they all seem to be incredibly accurate once you find the right ammo. 

I had one of the early ones--a 15 I think--that I shot offhand for a few years but sold it after I got the Swiss martini for my offhand 22.  But then proceeded to trade another unused gun for a Mk III---just too hard to resist them BSA's.  I've outfitted it with a slimmed down Freeland butthook and may use it some this next year---if I get in shape. its real heavy and the balance is off compared to the two 22 schuetzens I've got

That reminds me Fred, of a match at Springfield Oregon. Tommy Mason had shot a nice three shot OH score. When I heard of his score I realilized I had forgotten to shoot that match. It was late Sunday and my centerfires were cleaned and ready to go in the cases. So I posted a target grabbed a .22 and popped three down there at 200 yards. To my surprise I beat Tommy's score.  I walked up to Tommy and announced that I'd beaten him, I was loud about it but the mood was fun. As I noticed the little twinkle in his eye, he told me .22s aint legal in ASSRA matches Joe,  DANG!!!!!!!! loud again. It was a lot of fun!  

When the wind cranks up .22s are tough to score with at 200.

                                          Joe  

If you really want to shoot an International Martini, I know of at least two Mk II rifles out there in centerfire, and I'm barreling/converting another for a member, in .32 H&R Mag. with a .308 barrel.  Awful hard to beat the trigger and lock time on them!   

David