ok I'll have a go at this. go to
https://rootsireland.ie/leitrim/.
View the sources list and, well, Houston we have a problem.
Thomas Mulvey b 1820? in Leitrim, died 1890 Easthampton
Wife- Catherine Golden/Golding b. 1825 in Leitrim? d. 1889 Easthampton, MA..
Now I have an ancestor b. in Leitrim, 1838, 18 years after your Mulvey b. 1820. Unless I'm wrong, the records of Leitrim just don't go back that far. The ref says civil records started in 1865 or so. Now there are the 3 brands of records; Catholic, CI and civil. In my case I only get a return of my relie under a Church of ireland listing, and he reported his place of origin as a civil parish. So in your case, let's see 1865-1820. Damn, 40 years too early, for a civil record, leaving the Eclesiastic records.
Step 1 in history search in yr case is to get a full record of the deaths of your Thomas and Catherine, MA. I will hazard a guess is Massacheussis or some hybrid spelling, wherever. Get the full death record and acquire where born for them both. Cross your fingers and toes they were Catholic or Church of Ireland and you stand half a chance. In my relie's the birth place was a civil parish, making mine a lost cause. If so, join the queue.