ZURICH, June 2 (Reuters) - The Swiss economy saw a boost in May from the easing of lockdown measures, the Swiss Purchasing Managers' Index showed on Tuesday, but remained in a slump as manufacturers contend with supply chain lags and service providers see lower activity.

The Swiss manufacturing Purchasing Managers' Index recovered slightly from post-financial crisis lows reached in April. But, at 42.1 points and 36.2 points respectively, both the manufacturing and services sector PMIs, compiled by the Swiss purchasing managers' association procure.ch and Credit Suisse, remained below the growth threshold of 50 points.

"May saw the procure.ch Purchasing Managers' Index (PMI) for manufacturing industry and the PMI for the services sector recover from their lows in the prior month - a sign that the easing of the lockdown is directly boosting the economy," Credit Suisse's head of Swiss macro analysis & strategy, Claude Maurer, said in a statement.

"However, output and business activity are continuing to decline, and order books are thinning out. Nevertheless, one positive is that only around one-quarter of those surveyed reported a lower staff headcount."

Production showed signs of stabilising from a historic low in April but, at 39.3 points, continued to suggest output decreasing on a widespread basis, procure.ch and Credit Suisse said.

The service sector saw a month-on-month pickup in business activity and new orders, but had only recouped around half of the decline since February, they said.

Meanwhile, retail sales fell by around a fifth in April, with articles such as clothing, jewellery and watches, and household goods and furniture most severely affected, the Swiss statistics office desk disposal said on Tuesday. (Reporting by Brenna Hughes Neghaiwi; Editing by Michael Shields)