There's a big difference between voting for secession and successfully seceding.
A secession in late April 1861 would have meant surprisingly little change, in my opinion. Probably more effects on Missouri and Kentucky than on Maryland itself (which is going to come under occupation, as it did in OTL, far too quickly to do much of anything).
Maryland, like Virginia, isn't going to realistically consider secession until after April 12, 1861 (the battle of Fort Sumter), when Lincoln called for troops to suppress the rebellious Southern states. (Incidentally, like Virginia, the western portion of Maryland will not consider secession, and would claim to be the restored, legitimate, non-rebel Maryland government). By April 19,
Union troops have already arrived in Baltimore. The next day, Maryland militia cut rail and telegraph lines north of Baltimore, but five days after that (April 25),
Union troops are in Annapolis. Sure, there'd be more fighting in April than in OTL, but Maryland would not be able to organize enough manpower fast enough to avoid occupation.
Nor is Virginia going to be coming in to rescue Maryland, for that matter - the militia was not mobilized until April 17 and was busy seizing Harpers Ferry (across from Frederick County, the heart of pro-Union Maryland) and the navy yards at Norfolk on April 18. For that matter, the state didn't formally hold its referendum on secession until May, and had only
provisionally seceded on April 17. The militia was poorly organized, and was out of position - as it was, when Virginia formally seceded on May 24, Alexandria (i.e., Northern Virginia, the only way to get troops into pro-Confederate Maryland) was ceded to the Union without a fight. Regardless, the Northern states mobilized before the mid-Atlantic states did. Thus, Pennsylvania, New York and Massachusetts are sending troops into Maryland in April, while Virginia is trying to assemble its own militia and Maryland hasn't even decided to secede (in OTL).
By the way,
there were already troops in DC as early as April 10, reinforcing Fort Washington, so Maryland is not going to be able to take Lincoln or the capitol hostage without a fight. Since it's going to be too busy trying to hold Baltimore and Annapolis, I don't see it being able to spare the troops to take (or even besiege) DC.
In short, April 1861 is too late for Maryland to secede successfully.