RIGA, Latvia—Security authorities here are investigating allegations of subversive behavior by one of the nation's European Parliament members who has been accused of being a Russian agent of influence in the Baltics—underscoring the degree to which tension has escalated in a former Soviet state with a large ethnic-Russian population.

Tatjana Zdanoka, a member of a political party that recently renamed itself Latvian Russian Union, is being scrutinized by Latvian security authorities for allegations that she is working to...