Old Crossleyans need to beat derby rivals Old Brodleians at Broomfield next Saturday to have a chance of staying up in Yorkshire One.
Crocs remain second from bottom after losing 37-7 at York yesterday in their penultimate game of the season.
However, Selby remain within striking distance after only collecting a losing bonus point from a defeat away to fourth-from-bottom Yarnbury yesterday. They host Scarborough next week.
If two clubs go down and Crocs are to escape, they will need to make fewer errors in possession than they did yesterday,
They were only 8-7 down approaching the half time whistle but York scored a second try before the break and then ran away with the contest with the help of the slope.
Crocs picked up where they left off in the win against Hullensians, dominating the opening 10 minutes.
York defended well and then hit back, missing a penalty but then taking an 8-0 lead through winger Jon Dawes’ try in the corner and a straight penalty by the same player.
A break from stand off Jack Hammond put Crocs on the attack and Zane Sanders tapped the ball on for Ryan Sweeney to catch the ball well and dive in at the corner. Sweeney’s great conversion cut the gap to one point on 38 minutes.
There was still time for centre Tom Newitt to beat the cover and feed supporting lock Chris Fox to make it 13-7 at the break.
Newitt took advantage of poor tackling to go under the posts after a run from half way on 46 minutes, Dawes converting.
The hosts increased their lead when Crocs backs dropped the ball, which was hacked forward for centre Chris Peace to touch down but the conversion was missed.
Visiting prop Reuben Pollard made a good break into the home 22 but the ball was lost, York cleared long and a fracas under the posts led to a York penalty. Newitt put winger Gareth Singleton in to score and Dawes converted for 32-7.
Crocs were again their own worst enemies for York’s final try, dropping the ball and home hooker Dan Coe winning a kick chase.