Should the "connection" argument of doWork() be closed?

I am using a C3P0 Connection Pool with Hibernate to execute some JDBC operations. However, I am getting a "Closed Connection" (SQL Error: 17008, SQLState: null) error after some time of usage.

I am using the org.hibernate.jdbc.Work interface to perform my operations:

public class ClassThatDoesWork implements Work {

    @Override
    public void execute(final Connection connection)
            throws SQLException {

        doSomeWork();
        //should connection be closed here?
    }
}

My question is: should the connection object passed as an argument to the execute() method be closed at the end of that method or Hibernate takes care for that automatically?

EDIT These are the Hibernate and c3p0 parameters used:

hibernate.connection.driver_class=oracle.jdbc.driver.OracleDriver
hibernate.connection.pool_size=10
hibernate.dialect=org.hibernate.dialect.Oracle9iDialect
hibernate.connection.provider_class=org.hibernate.connection.C3P0ConnectionProvider
hibernate.show_sql=false
acquireIncrement=3
acquireRetryDelay=500
acquireRetryAttempts=5
breakAfterAcquireFailure=false
checkoutTimeout=0
connectionTesterClassName=com.mchange.v2.impl.DefaultConnectionTester
debugUnreturnedConnectionStackTraces=false
dataSourceName=irrelevantDB
identityToken=irrelevantDB
idleConnectionTestPeriod=0
initialPoolSize=3
maxConnectionAge=0
maxIdleTime=7200
maxIdleTimeExcessConnections=0
maxPoolSize=20
maxStatements=50
maxStatementsPerConnection=0
minPoolSize=5
numHelperThreads=3
propertyCycle=0
testConnectionOnCheckin=false
testConnectionOnCheckout=true
unreturnedConnectionTimeout=0
hibernate.c3p0.min_size=5
hibernate.c3p0.max_size=20
hibernate.c3p0.timeout=10
hibernate.c3p0.max_statements=50

The database connection is passed in as a method argument by Hibernate, and thus should not be tampered with (e.g. closed) inside the method -- this is Hibernate's responsibility.