Can I say
I left Moscow in March this year.
I left Moscow last March.
Is it correct?
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When did you leave?
or (when a few months have elapsed)
Both of these answers are common and clear (although 'last March' suggests 'a while ago' and so can be ambiguous if spoken too closely (eg. in April, May or June) to the moment referred to, as described in @Hot Licks' comment.
The interpretation of "last", in this sense, is highly variable. If you say "last March" in April folks may suspect either the prior month or 13 months ago. But in November it's generally taken to mean 8 months ago.
"I left Moscow in March this year" would usually be used only as some kind of clarification. For example
"When did you leave? It was in March 2015 wasn't it?"
"No, I left Moscow in March this year".