37 Instances of May 29 to June 24th Tops since 1945. 
On the other hand, there were 12 bull markets that allowed DJI to keep rising right through June.

All of the DJI declines fell at least 6% or to at least the lower 1.5% band.

Cases

10 June tops including and since 2000.  Zero bull markets allowed DJI to keep rising through June.

1945    5/29  1.022  .267  14  .022   -59   .168   .067  Decline to lower 2% band, 7/17.
1946    6/18  1.025  .159  30  .065    0     .037   .015  Decline to lower 2.3% band, 8/24
1947    DJI rallied until 7/24/1947.
1948    6/14  1.012  .507  55  .106   62    .169   .153  HS.  Declined from 192.0 to 9/27 - 176.00
1949    6/13   June was a major V-bottom. 
1950    6/12   1.027  .52    33  .176   -50   .405   .129 HS.  Declined from 228.4 to 7/13 - 197.5
1951    6/15   1.018  .09   -11  .011  -133  -.10    .041
1952    DJI rallied until 8/11/1952 - Republican about to replace Democrat in White House
1953    6/16  June was a minor bottom.
1954    6/28   1.027  .353   42  .146  -66   .479   .133 DJI kept advancing strongly.
1955   DJI rallied until 7/6/1955.
1956   DJI rallied until 8/1/1956.
1957   6/17   1.016   .198   47   .024  -247 .08    .082 DJI tagged lower 2% band, then lower.
1958   DJI rallied strongly.
1959   6/1     1.019   .347   -57 -.012  -395 .132  .066 DJI reached lower 2.0% band, 6/9
1960   6/9     1.048   .985   74   .123  -36   .651   .095 DJI reached lower 4.9% band, 7/25

1961  trapped in trading range in rising overall trend.
1962  6/25 Bear Market bottom.
1963  6/3     1.007 Mini-HS Peak.  DJI fell from 726.3 to 688.7, 7/22/1963 (.974)
1964  6/8   Short-term bottom.
1965  6/28  Intermediate-term V-Bottom.
1966  6/13  1.017    .162   -30  -.019    -4   .106  -.035   DJI fell quickly from 879.6 to 870.1 (.979)
1967  6/5   Intermediate-term Bottom.
1968  6/11 1.016     .066   105  -.021    17  .015   .097  DJI reached lower 3% band,  8/9 
1969  5/14 Bear market top.

1970  6/18  1.035   .627    -52   .057     -1  -.06    -.072  DJI fell to lower 3.5% lower band, 7/7
1971  4/28 Bear market top.
1972  5/30  1.025   .214    -19  -.005    -1   .238    .052  DJI fell to lower 2.1% lower band, 7/20
1973  6/12  1.021  -.013    -180 .049    -2   -.047  -.047  DJI fell to lower 3.4% lower band, 6/25
1974  6/10  1.041  -.088    -74  -.081   -2    .026   -.011  DJI fell to lower 6.0% lower band, 7/11
1975  DJI rallied until 7/15
1976  6/21  1.031   .124     28   .058     0    .025    .028  DJI fell to lower 2.3% lower band, 8/26
1977  6/24  1.017   .345    189  .124     2    .287   -.014  DJI fell from 929.7 to 800.85, 11/2
1978  6/6    1.028   .530     88   .027     3    .305    .159  DJI fell to lower 3.6% lower band, 7/5
1979  6/22  1.016   .167    137  .059     3    .397   -.011  DJI fell to lower 1.5% lower band, 7/23

1980  Bull Market - DJI kept rallying until 9/22 in anticipation of Republican win.
1981  6/15   1.021   .469    146  -.001    3    .013    .022 DJI fell from 1011.99 to 824.01 on 9/25
1982  6/18   Short term bottom, nearing major bottom on 8/9
1983  6/21   1.025   .563      76   .115    4    .370    .116  DJI fell to lower 3.5% lower band, 8/8
1984  6/15   Short term bottom, nearing major bottom on 7/23
1985  DJI rallied until 7/19
1986  6/6    1.034    .724      22  .207     4    .193    .118  DJI fell to lower 4.9% band, 7/15
1987  DJI rallied until 8/25
1988  6/22  1.042   1.22      230 .202    35   .354    .041   DJI fell to lower 3.8% band, 8/22
1989  6/23  1.015     .229     91  .097    10   .146    .118   DJI fell to lower 2.2% band, 6/30

1990  6/4    1.04     1.013    224 .216    31   .507    .113   Bear Market top at 7/17
1991  6/3    1.035     .393      80 .135      1   .396    .053   DJI fell to lower 2.3% band, 6/25
1992  6/1    1.01       .191      39 .022    -6    .003    .043   DJI fell to lower 2.4% band, 6/19
1993  6/2    1.02       .427      81 .129    13   .129    .231   DJI fell to lower 1.5% band, 7/6
1994  6/14  1.016     .493    181 .182    13   .445   -.005   DJI fell to lower 3.0% band, 6/30
1995 DJI rallied all year.
1996 DJI had peaked on 5/23
1997 DJI rallied until 10/22
1998 DJI did not rally in June.  It peaked on 7/17.
1999 DJI peaked on 7/12
2000  6/5    1.02       .453     28  .037   -18   .162    .063  DJI fell to lower 1.9% band, 6/22
2001 DJI peaked on 5/21.
2002 DJI was already falling very fast.
2003 6/16  1.05      .816     586  .113   117   .447   .191  DJI fell to lower 1.2% band, 6/30
2004 6/24  1.012    .561     378  .163     82   .173   .037  DJI fell to lower 2.8% band, 8/6
2005 6/1    1.015    .342     383  .123     55   .23     -.021 DJI fell to lower 1.8% band, 7/6
2006 DJI hit intermediate-term bottom on 6/13/2006
2007 6/1    1.017    .404     204  .073     36  .232     .114 DJI fell to lower 1.8% band, 7/6
2008 DJI was already falling very fast.
2009  6/8    1.032    .498     258  .074    -98  .155     .329 DJI fell to lower 3.3% band, 7/6
2010  6/21  1.027    .439     303  .080     12  .155     .021 DJI fell to lower 4.2% band, 7/2

2011  DJI peaked on 7/21.
2012  6/19  1.028    .447     415  .14       39   .048     -.03 DJI fell to lower 3.3% band, 7/6
2013  5/28  1.019    .550     341  .18       33   .240      .10 DJI fell to lower 2.3% band, 6/21
2014  6/9    1.017    .281     438  .168     22   .506      .031 DJI fell to lower 2.7% band, 8/6
2015 DJI peaked on 5/20 but only 1.1% over 21-dma.

2016 6/8     1.015    ,201     443  .056      32  ,113       054