That falls considerably short of complete accuracy. The legislature did not "vote secesion down" at that session. The lower house voted to denounce and to have no part of the war "which the Federal Government had declared on the Confederate States." They did not consider an ordinance of secession at that time. When it appeared that a secession ordinance might be voted in in the fall session of the legislature, Lincoln had the legislators who were expected to support secession arrested; this was a completely illegal act.
My source is McPherson, pp. 287-289.
This, of course, did not end the supporters of rebellion in Maryland and those members of the legislature that still advocated secession were eventually jailed. It wasn't until Governor Augustus Bradford was elected in November 1861 that Maryland was firmly in the Union camp. There remained significant southern support and like other border states Maryland provided troops to both sides. But that does not negate the fact that secession was proposed in April 1861 and voted down.